In Exercises 1-16, use the graph of y = f(x) to graph each functi...

Question

In Exercises 1-16, use the graph of y = f(x) to graph each function g.

Graph showing points (1, -3) and (4, -3) with line segment for y = f(x).

g(x) = −ƒ( x/2) +1

Accepted Answer

Grab the function G. By using the graph of Y equals F. Of X. Where our function is G. X equals negative F. X over three plus four. We want to find our transformations. The first thing we'll look at is inside the parentheses we have X over three. Or in other words we have one third X. Inside this means we have a horizontal stretch or shrink In this case are 1/3 is less than one. So we have a horizontal stretch. I was on a stretch of 1/3. So if you look at our points We're going to multiply all of our points not by 1/3 but by three to get rid of the one thirds. Our appointment now is one negative three and four negative three multiply everything by three. We will get three negative three And 12 -3. No we want to look at our next transformation. We have a negative in front of the F. Of X. That means we're going to flip over the X. Axis. In other words we'll turn our wives from negative to positive. We don't have three negative three. I'm sorry not three negative three but three positive three and 12 positive three. Finally we have a plus four on the outside That plus four tells us we have a vertical shift now Uncle shift of four and we're going up So we're gonna add 4 to all of our wives. We're now left with 37 and 7. Let's go ahead and find the graph that has the points 37 and 12 7. If you look go all the way down, we notice graph D. Has a 0.37 and 12 7. That means our answer is D. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 1-16, use the graph of y = f(x) to graph each function g.
g(x) = −ƒ( x/2) +1

Key Concepts

Function Transformation

Horizontal Stretch

Reflection Across the X-Axis

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