Chapter 4, Problem 1MC

Determine whether the statement is true or false.

The y-intercept of the graph of the function P(x) = 5 − 2x³ is (5, 0). [4.2]

To determine

Whether the given statement is true or false.

Answer to Problem 1MC

The given statement is false.

Explanation of Solution

The statement is “The y intercepts of the graph of the function $P\left(x\right)=5-2x^3$ is $\left(5,0\right)$”.

Note that the x-intercepts of the graph of a function is the points at which the curve intersects the x-axis and the y-intercepts of the graph of a function is the points at which the curve intersects the y-axis.

In order to find the y intercept, substitute $x=0$ and simplify.

$\begin{array}{c}P\left(0\right)=5-2{\left(0\right)}^3\\ =5-0\\ =5\end{array}$

Therefore, the y intercept is $\left(0,5\right)$.

Thus, the statement is false.