From a blank screen, follow the above keystrokes to graph your equations.
IM1.5.7 Calculator Skills
See an equation as two functions
Let's look at our opening problem again: [math]|x+2|-3=0.5x+1[/math][br]Think about this problem as two functions, one for the left side and one for the right side:[br][math]f\left(x\right)=|x+2|-3[/math] and [math]g\left(x\right)=.5x+1[/math]. Follow the directions for solving this equation on your calculator, and enter the solutions below.
Keystrokes
Graphed equations
This is what your screen should look like now.
Solving with a table
Press the keys above to see a table of values for both functions. Where do the functions have the same value?
Solving with a graph
Press the keys above, then use the arrow keys to move the cursor close to an intersection point, and press enter three times.
Try it on your own
Equation: [math]|0.5x|-5=-|x-3|+4[/math][br]1. Write the two functions you will graph on your calculator.[br]2. Write the intersection points of the two functions.[br]3. The original equation is true when x= _____ or _____.
4. Find the solutions to the equation [math]-|x-3.5|+4=-0.25x-1[/math]
5. The graphs of [i]f[/i], a function that involves taking an absolute value, and [i]g[/i] a linear function, are shown above. Both functions are defined over all real values for x. Tami concluded that the equation [i]f(x)=g(x)[/i] has no solution. Do you agree or disagree? Explain your reasoning.[br]