If a horizontal line can intersect the curve at more than one point, then the inverse is not a function.
No
Practice makes perfect
We can use the Horizontal Line Test to determine whether the inverse of a function is also a function. To do this with the given function, we will first make a table of values to graph it. When making a table of values, make sure to use a variety of points, including negative and positive values.
x
3x^2
h(x)
- 3
3( - 3)^2
27
- 2
3( - 2)^2
12
- 1
3( - 1)^2
3
0
3( 0)^2
0
1
3( 1)^2
3
2
3( 2)^2
12
3
3( 3)^2
27
Now we can plot the obtained points and connect them with a smooth curve. Consider also that this is an even-degreepolynomial with a positive leading coefficient. This tells us about the end behavior of the function.
&f(x) → + ∞ as x → - ∞
&f(x) → + ∞ as x → + ∞
Let's draw the function.
Finally, we can perform the Horizontal Line Test. If the horizontal lines intersect the graph once, then the inverse is also a function. Conversely, if there is even one horizontal line that intersects the graph more than once, then the inverse is not a function.
We can see above that there are horizontal lines that intersect the curve at more than one point. Therefore, the inverse of the given function is not a function.
