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^4+2x-1
g(x)
- 3
-3( - 3)^4+2( - 3)-1
- 250
- 2
- 3( - 2)^4+2( - 2)-1
- 53
- 1
-3( - 1)^4+2( - 1)-1
- 6
0
- 3( 0)^4+2( 0)-1
- 1
1
- 3( 1)^4+2( 1)-1
-2
2
- 3( 2)^4+2( 2)-1
-45
3
-3( 3)^4+2( 3)-1
-238
Now we can plot the obtained points and connect them with a smooth curve. Consider also that this is an even-degreepolynomial with a negative leading coefficient. This tells us about the end behavior of the function.
&g(x) → - ∞ as x → - ∞
&g(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.
