The accompanying figure shows the graph of a function f(x) wit...

Question

The accompanying figure shows the graph of a function f(x) with domain [0,2] and range [0,1]. Find the domains and ranges of the following functions, and sketch their graphs.

c. 2f(x)

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says graph the given function by applying transformations to the shown graph. Also find the domain and range. Below the problem we're given a graph of a function Y is equal to H X, and this function is parabolic in shape and begins at the origin, has a local minimum at 1 minus 1 and ends at the point of 2.0. And we're given the function of 3 multiplied by H of X, and we're also given an empty graph on which to plot this function. So we need to draw the graph of the function 3 multiplied by H of X by using transformations. And so, since we have 3 multiplied by HFX as our function, what we'll need to do is multiply all the Y values in our original graph for HF X by 3. So, our graph of H of X starts at the origin. So when I multiply 0 by 3, which is going to be our Y value at the origin, I also get back 0, so we'll have a point at 0.0. The next point we'll look at is the local minimum, and that occurred at 1-1 for H of X. So we'll need to multiply that minus 1 by 3, and so we'll have a local minimum at 1.3 or a graph of 3 multiplied by H of X. And finally, our graph reaches the x-axis again when X is equal to 2. And so here we're going to have, again, ay value of 0, and we multiply 0 by 3, we also get back to 0. We'll have another point at 2.0. So now we'll just create another problem, but now it has a local minimum. At X X equal to 1, and Y is equal to minus 3. So, the graph that we have drawn on the screen is the graph 43 multiplied by HF X. So now we also need to find the domain and range of this function. So we'll start off by looking at the domain. So if we look at the possible X values that our function of 3 multiplied by H of X can take, we see that the X values range from 0 to 2. So our domain is going to be the closed interval, going from 0 to 2. Next, we'll look at the range. And if we look at the possible Y values, That our function 3 multiplied by H of X can take, the Y values range from 0 to -3. So, we'll have the close interval, going from -3 to 0 for our range. So those are the answers that we're looking for. So our domain is going to be the closed interval from 0 to 2, and our range is gonna be the closed interval from -3 to 0. So, I hope that this explanation has been useful, and I'll see you in the next video.

The accompanying figure shows the graph of a function f(x) with domain [0,2] and range [0,1]. Find the domains and ranges of the following functions, and sketch their graphs.

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c. 2f(x)

Key Concepts

Function Transformation

Domain and Range

Graph Sketching

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