Explore transformations of sin(x) by adjusting the sliders. What affect does each parameter seem to have on the shape of the graph?
Set the pronumerals 'a' and 'b' so that it has value of 1. Ensure that the other pronumerals (h,k) have a value of zero.
When the pronumeral 'a' has a value of 1 what do you notice?
When the value of 'a' is greater than 1 what is the effect on [math]y=sinx[/math] ?
Given that [math]f\left(x\right)=sinx[/math]. Describe how the graph of [math]g\left(x\right)=3sinx[/math] differs from [math]f\left(x\right)[/math].
a. For the graph [math]f\left(x\right)=sinx[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi[/math] . [br]b. For the graph of [math]g\left(x\right)=3sinx[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi[/math][br]c. How do the coordinates of [math]f\left(x\right)[/math]differ from [math]g\left(x\right)[/math]?
What effect does the value of 'a', when 'a' is a proper function have on [math]y=sinx[/math]?
a. What effect does assigning a value of a=-1 have on the parent function [math]y=sinx[/math]?[br]b. What effect does assigning values for the pronumeral 'a', of [math]a[/math] <-1, have on the parent function [math]y=sinx[/math]?[br]c. What effect does assigning values for the pronumeral 'a', of -1<[math]a[/math]<0, have on the parent function [math]y=sinx[/math]?
Amplitude is defined as the vertical dilation of a trigonometric function. [br]a. What would be the amplitude of [math]f\left(x\right)=5sinx[/math]?[br]b. What would be the amplitude of [math]f\left(x\right)=\frac{sinx}{4}[/math]?[br]c. What would be the amplitude of [math]f\left(x\right)=-sinx[/math]?[br]d. What would be the amplitude of [math]f\left(x\right)=3sinx-1[/math]?
Set the pronumerals 'a' and 'b' so that it has value of 1. Ensure that the other pronumerals (h,k) have a value of zero.
Given that [math]f\left(x\right)=sinx[/math] and [math]g\left(x\right)=sin2x[/math], explain the effect of the assigning the pronumeral 'b' the value of 2, on [math]f\left(x\right)[/math].
a. For the graph [math]f\left(x\right)=sinx[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi[/math] . [br]b. For the graph of [math]g\left(x\right)=sin2x[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi[/math][br]c. How do the coordinates of [math]f\left(x\right)[/math]differ from [math]g\left(x\right)[/math]?
When given that [math]f\left(x\right)=sinx[/math] and [math]g\left(x\right)=sin\frac{x}{2}[/math], explain the effect of the assigning the pronumeral 'b' the value of [math]\frac{1}{2}[/math], on [math]f\left(x\right)[/math]
a. For the graph [math]f\left(x\right)=sinx[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi,\frac{13\pi}{6},\frac{5\pi}{2},\frac{8\pi}{3},3\pi,\frac{13\pi}{4},\frac{7\pi}{2},\frac{23\pi}{6},4\pi[/math]. [br]b. For the graph of [math]g\left(x\right)=sin\frac{x}{2}[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi,\frac{13\pi}{6},\frac{5\pi}{2},\frac{8\pi}{3},3\pi,\frac{13\pi}{4},\frac{7\pi}{2},\frac{23\pi}{6},4\pi[/math][br]c. How do the coordinates of [math]f\left(x\right)[/math]differ from [math]g\left(x\right)[/math]?
When given that [math]f\left(x\right)=sinx[/math] and [math]g\left(x\right)=sin\left(-x\right)[/math], explain the effect of the assigning the pronumeral 'b' the value of [math]-1[/math], on the parent function.
a. For the graph [math]f\left(x\right)=sinx[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi[/math]. [br]b. For the graph of [math]g\left(x\right)=sin\left(-x\right)[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi[/math][br]c. How do the coordinates of [math]f\left(x\right)[/math]differ from [math]g\left(x\right)[/math]?
When given that [math]f\left(x\right)=sinx[/math] and [math]g\left(x\right)=sin\left(-2x\right)[/math], explain the effect of the assigning the pronumeral 'b' the value of [math]-2[/math], on the parent function.
a. For the graph [math]f\left(x\right)=sinx[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi[/math] . [br]b. For the graph of [math]g\left(x\right)=sin\left(-2x\right)[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi[/math][br]c. How do the coordinates of [math]f\left(x\right)[/math]differ from [math]g\left(x\right)[/math]?
Frequency is defined as the horizontal dilation of a trigonometric function and affects the period. [br]a. What would be the period of [math]f\left(x\right)=sin2x[/math]?[br]b. What would be the period of [math]f\left(x\right)=sin\frac{x}{4}[/math]?[br]c. What would be the period of [math]f\left(x\right)=2sin4x[/math]?[br]d. What would be the period of [math]f\left(x\right)=sin\left(-x\right)[/math]?
In the function given above assign the value of 1 to the pronumerals 'a' and 'b' and assign the value of 0 to 'h'.[br][br]Note for the parent function [math]f\left(x\right)=sinx[/math] the centre of this function is [math]y=0[/math] as we can write the parent function as [math]f\left(x\right)=sinx+0[/math]. This is an important point of reference when describing the effect of changing the value of the pronumeral 'k'.
Given that [math]f\left(x\right)=sinx[/math] and [math]g\left(x\right)=sinx+1[/math], explain the effect of assigning 'k' the value of 1 on the parent function [math]f\left(x\right)=sinx[/math].
Given that [math]f\left(x\right)=sinx[/math] and [math]g\left(x\right)=sinx-1[/math], explain the effect of assigning 'k' the value of 1 on the parent function [math]f\left(x\right)=sinx[/math].
a. For the graph [math]f\left(x\right)=sinx[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi[/math] . [br]b. For the graph of [math]g\left(x\right)=sinx+1[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi[/math][br]c. How do the coordinates of [math]f\left(x\right)[/math]differ from [math]g\left(x\right)[/math]?
a. For the graph [math]f\left(x\right)=sinx[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi[/math] . [br]b. For the graph of [math]g\left(x\right)=sinx-1[/math], find the coordinates for [math]x=0,\frac{\pi}{6},\frac{\pi}{2},\frac{2\pi}{3},\pi,\frac{5\pi}{4},\frac{3\pi}{2},\frac{11\pi}{6},2\pi[/math][br]c. How do the coordinates of [math]f\left(x\right)[/math]differ from [math]g\left(x\right)[/math]?
[math]g\left(x\right)=sinx+1[/math] is a transformation of the parent function [math]f\left(x\right)=sinx[/math]. How we describe the transformation is in reference to how the centre of the parent function [math]y=0[/math] is vertically translated up or down.
A vertical translation is defined by the number of units the centre of the parent function is moved up or down. [br]a. What would be the vertical translation of [math]f\left(x\right)=sinx+2[/math]?[br]b. What would be the vertical translation of [math]f\left(x\right)=sinx+\frac{1}{2}[/math]?[br]c. What would be the vertical translation of [math]f\left(x\right)=sinx-3[/math]?[br]d. What would be the vertical translation of [math]f\left(x\right)=sinx-\frac{1}{4}[/math]?
In the function given above assign the value of to the pronumerals 'a', 'b' and 'h' and assign the value of 0 to 'k'.[br][br]Note for the parent function [math]f\left(x\right)=sinx[/math] when considering the transformed function in the form of [math]g\left(x\right)=sin\left(x+k\right)[/math] the pronumeral 'k' represents a value which has been either added or subtracted from the x-coordinate.
Given that [math]f\left(x\right)=sinx[/math] and [math]g\left(x\right)=sin\left(x-\frac{\pi}{2}\right)[/math], explain the effect of assigning 'k' the value of [math]\frac{\pi}{2}[/math] on the parent function [math]f\left(x\right)=sinx[/math].
Given that [math]f\left(x\right)=sinx[/math] and [math]g\left(x\right)=sin\left(x-\pi\right)[/math], explain the effect of assigning 'k' the value of [math]\pi[/math] on the parent function [math]f\left(x\right)=sinx[/math].
Given that [math]f\left(x\right)=sinx[/math] and [math]g\left(x\right)=sin\left(x+\frac{\pi}{2}\right)[/math], explain the effect of assigning 'k' the value of [math]-\frac{\pi}{2}[/math] on the parent function [math]f\left(x\right)=sinx[/math].
Given that [math]f\left(x\right)=sinx[/math] and [math]g\left(x\right)=sin\left(x+\pi\right)[/math], explain the effect of assigning 'k' the value of [math]-\pi[/math] on the parent function [math]f\left(x\right)=sinx[/math].
a. For the graph [math]f\left(x\right)=sinx[/math], find the coordinates for [math]x=0,\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi,\frac{5\pi}{2},3\pi[/math] . [br]b. For the graph of [math]g\left(x\right)=sin\left(x-\frac{\pi}{2}\right)[/math], find the coordinates for [math]x=0,\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi,\frac{5\pi}{2},3\pi[/math][br]c. How do the coordinates of [math]f\left(x\right)[/math]differ from [math]g\left(x\right)[/math]?
a. For the graph [math]f\left(x\right)=sinx[/math], find the coordinates for [math]x=0,\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi,\frac{5\pi}{2},3\pi[/math] . [br]b. For the graph of [math]g\left(x\right)=sin\left(x+\frac{\pi}{2}\right)[/math], find the coordinates for [math]x=0,\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi,\frac{5\pi}{2},3\pi[/math][br]c. How do the coordinates of [math]f\left(x\right)[/math]differ from [math]g\left(x\right)[/math]?
a. For the graph [math]f\left(x\right)=sinx[/math], find the coordinates for [math]x=0,\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi,\frac{5\pi}{2},3\pi[/math] . [br]b. For the graph of [math]g\left(x\right)=sin\left(x-\pi\right)[/math], find the coordinates for [math]x=0,\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi,\frac{5\pi}{2},3\pi[/math][br]c. How do the coordinates of [math]f\left(x\right)[/math]differ from [math]g\left(x\right)[/math]?
a. For the graph [math]f\left(x\right)=sinx[/math], find the coordinates for [math]x=0,\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi,\frac{5\pi}{2},3\pi[/math] . [br]b. For the graph of [math]g\left(x\right)=sin\left(x+\pi\right)[/math], find the coordinates for [math]x=0,\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi,\frac{5\pi}{2},3\pi[/math][br]c. How do the coordinates of [math]f\left(x\right)[/math]differ from [math]g\left(x\right)[/math]?
The phase of a trigonometric function results in a horizontal translation of the trigonometric is defined by the number of radians the parent function is moved left or right of the y-axis. [br]a. What would be the horizontal translation of [math]f\left(x\right)=sin\left(x+\frac{3\pi}{2}\right)[/math]?[br]b. What would be the horizontal translation of [math]f\left(x\right)=sin\left(x-2\pi\right)[/math]?[br]c. What would be the horizontal translation of [math]f\left(x\right)=sin\left(x-\frac{\pi}{4}\right)[/math]?[br]d. What would be the horizontal translation of [math]f\left(x\right)=sin\left(x+2\pi\right)[/math]?