Question

Create a graph that has the following intercepts. Make sure to label each of the intercepts on

the graph, as well as the axis on your graph.
y=-3, x = 5, y = 3

Answer 1

see below for the graph

Explanation:

The desired graph has two y-intercepts and one x-intercept. It is not the graph of a function.

Here's one way to get there.

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Start with the parent function y = |x| and scale it down so that it has a y-intercept of -1 and x-intercepts at ±1.

Now, it is ...

f(x) = |x| -1

We want to scale this vertically by a factor of -5. this puts the y-intercept at +5 and leaves the x-intercepts at ±1.

Horizontally, we want to scale the function by an expansion factor of 3. The transformed function g(x) will be ...

g(x) = -5f(x/3) = -5(|x/3| -1) = -5/3|x| +5

This function has two x-intercepts at ±3 and one y-intercept at y=5. By swapping the x- and y-variables, we can get an equation for the graph you want:

x = -(5/3)|y| +5

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Comment on this answer

Since there are no requirements on the graph other than it have the listed intercepts, you can draw it free-hand through the intercept points. It need not be describable by an equation.