In Exercises 17-32, use the graph of y = f(x) to graph each funct...

Question

In Exercises 17-32, use the graph of y = f(x) to graph each function g.

Graph of y = f(x) with points (2, 0) in red and (0, -8) in blue.

g(x) = f(-x)+1

Accepted Answer

Graft function H S in the graph of Y equals F of X. And so we have our graph here and we have our transformation. Our transformation is F negative X plus seven. This transformation implies a couple of things. You have a negative end with the X. That means we're going to flip over the Y axis. Other words, we're doing horizontal flip because of our negative but also shifting up seven units because of R plus seven. So we have a vertical shift of seven. Now we want to determine what our vertex and X intercept are on the vertex Is shifted up by seven hits as flipped over the X axis. I'm sorry, the Y axis rather. So we have zero negative eight as our vertex right now, let's go ahead and flip over the Y axis. That means we turn our xnegative. But Since its zero, we still have 0 -8 after the horizontal flip, now we'll go ahead and shift this up by seven. We're adding seven to the white. So we get zero negative one shift. So our new vertex is at 0 -1. Let's go ahead and find our x intercept Well, let's say we have Y equals X -HX one, N plus one. I'm sorry, that's actually minus K. So it's minus negative what X minus H to the N minus K. And so I'll actually erase each other there. Replace it with what we know is Our X. Ray Vertex zero. Now the X intercept will be when are Y is equal to zero? Saucy zero equals X minus zero to the end plus one. I'm gonna leave that in there because we know this is some odd function. You still know what these exponents. So sleeping as in for now find our X intercepts. We'll go ahead and solve for X subtract one, subtract one to get negative one equals X to the end. Now we don't know what are in this, but we know this is some odd function in an odd function. The root of a negative number remains negative. So we'll just say this X is equal to negative one because it's not function. Now we have our X intercept as native 10. So we need to find the graph that has two points zero, negative one and negative 10. If you look at the graphs answer A is a graph we're looking for, we have our vertex zero, negative one X intercept of negative one is here. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 17-32, use the graph of y = f(x) to graph each function g.
g(x) = f(-x)+1

Key Concepts

Function Transformation

Reflection Across the Y-Axis

Vertical Shift

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