Checking Rewritten Equation for y=-3f(-2x+4)+5

[aisha]

My question says the graph of the function y=f(x) is below Sketch the graph of y=-3f(-2x+4)+5 I just want to make sure I rewrote the equation correctly into the form af[k(x-p)]+q
I got y=-3f[-2(x-(2)]+5 ? I am not sure if my signs are correct. Can someone please check for me

 

[James R]

You're right.

 

[wais]

First of all, great job on rewriting the equation in the form of af[k(x-p)]+q! This is the correct form for a function in which the graph has been horizontally or vertically stretched, compressed, or shifted.

To check if your equation is correct, let's break it down into parts. The first thing we can check is the value of "a". In the original equation, y=-3f(-2x+4)+5, the value of "a" is -3. In your rewritten equation, y=-3f[-2(x-(2)]+5, the value of "a" is also -3. So, the value of "a" is correct.

Next, let's check the value of "k". In the original equation, the value of "k" is -2, since the expression inside the parentheses is -2x+4. In your rewritten equation, the value of "k" is also -2, since the expression inside the square brackets is -2(x-2). So, the value of "k" is also correct.

Moving on to "p", in the original equation, the value of "p" is 2, since the expression inside the parentheses is -2x+4. In your rewritten equation, the value of "p" is also 2, since the expression inside the square brackets is x-(2). So, the value of "p" is correct as well.

Lastly, let's check the value of "q". In the original equation, the value of "q" is 5, since it is the constant term added at the end. In your rewritten equation, the value of "q" is also 5, since it is added at the end as well. So, the value of "q" is also correct.

Overall, it looks like you have rewritten the equation correctly! Great job! Just remember to pay attention to the signs when dealing with negative numbers and you should be good to go. Keep up the good work!