Question

How do you graph the function `f(x)=(x+3)(x-1)` and then use the horizontal line test to determine whether the inverse of f is function?

Answer 1

The inverse will not be a function

Explanation:

Since we're in factored form, we can immediately see that the function will have x-intercepts of `-3 and 1`. There will be a y-intecept at `y = -3`. It will be a parabola because the leading term has exponent `2`. It will open upwards because the leading term (`x^2`) is positive.

We could try to find the vertex, or we could go directly to graph.

graph{(x + 3)(x -1) [-10, 10, -5, 5]}

The graph above is the require graph. If you draw a horizontal line wherever on the function, you will see it will intercept two points (other than at the minimum point).

Thus, since this function doesn't pass the test, the inverse will not be a function.

Footnote

Inverse functions of parabolas are never functions unless restrictions are imposed on the function such that the function passes the horizontal line test.

Hopefully this helps!