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) showing points (-2,0), (0,-4), and (2,0) for transformations.

g(x) = f(x-1)+2

Accepted Answer

Welcome back. I am so glad you're here. We are given a function. Were given the graph of Y equals F of X. That's this graph right here. And we're asked to graph H of X. And we're told that H of X equals F of parentheses X plus five and parentheses minus five. So we need to find the difference between these two functions to see what is going on with our H of X. How do we need to shift our given function graph here? So let's look and see what the differences are. Well, the first one we see from our F. Of X, this has an F. Of X plus five, that X plus five, that's inside the parentheses. It's inside the function indicates a horizontal shift because it's happening directly to the function. And because we're adding five, the horizontal shift is to the left five units. So that's one of our shifts. So looking back at our Y equals f of X. R H of X is going to the left five units. So the X value will be changing from zero to negative five. Let's see what else we've got. Now. We've got this other shift here, this -5 on the end, that's not inside of our function, it's not happening directly to the f. Of X comes afterward. So because that's outside of the parentheses that indicates a vertical shift. And because we are subtracting five it is going to be down five units. So looking back at our Y equals F of X for our H of X. Another shift is that it's going to go down five units and we are going to have for our new Y. Value. The old Y. Value here was negative four. Now it's going to be down five more. It's going to be negative nine. So our H. Of X. We are looking for something that is going to meet at negative five negative nine. We're going to have it come together at negative five negative nine. So let's look for a negative five negative nine. And now we can go take a journey through our answer choices see what works for our H. Of X. Okay for this answer choice A. They have got a center here it comes together. That V shape comes together for the function at negative 51 nope. We're looking for negative five negative nine. Sorry answer choice A. We are moving on. I answer choice B. And those lines this function comes together at 51. That's not what we're looking for. We're looking for negative five negative nine. Sorry answer choice B. You are not helpful right now. I need to rewrite this down here. We have negative five negative nine. And answer choice C. What have you got? Hey look at that negative five negative nine. And we can see the answer choice D. That's five negative nine. That doesn't work. So D also doesn't work and answer choice. C. Does come together with this function at negative five negative nine. Well done. We'll catch you on the next one.

In Exercises 17-32, use the graph of y = f(x) to graph each function g.
g(x) = f(x-1)+2

Key Concepts

Function Transformation

Horizontal Shifts

Vertical Shifts

Watch next