To find the y-intercept of the function [tex]\( y = x^3 + 2x - 5 \)[/tex], you need to determine the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is equal to 0. The y-intercept is the point at which the graph of the function crosses the y-axis, which occurs when [tex]\( x = 0 \)[/tex].
Here are the steps to find the y-intercept:
1. Start with the function:
[tex]\[
y = x^3 + 2x - 5
\][/tex]
2. To find the y-intercept, set [tex]\( x = 0 \)[/tex]:
[tex]\[
y = (0)^3 + 2(0) - 5
\][/tex]
3. Simplify the expression:
[tex]\[
y = 0 + 0 - 5
\][/tex]
[tex]\[
y = -5
\][/tex]
Therefore, the y-intercept of the function [tex]\( y = x^3 + 2x - 5 \)[/tex] is [tex]\(-5\)[/tex]. The point where the graph intersects the y-axis is [tex]\((0, -5)\)[/tex].
