N/A — Exam

Question 75 • Algebra II

Which of the following graphs could be the graph of the function f of x is equal to x cubed plus 8 ?

Answer

Image with description On a coordinate plane with x and y axes marked from negative 10 to 10, a polynomial graph is drawn. It starts from quadrant 2, passes through (negative 0 point 2 comma 10), crosses the y axis at (0 comma 8), crosses the x axis at (2 comma 0) and moves to quadrant 4 through the point (4 comma negative 8).

Image with description On a coordinate plane with x and y axes marked from negative 10 to 10, a polynomial graph is drawn. It starts from quadrant 1, passes through (1 comma 10), crosses the y axis at (0 comma 8)curves down and crosses the x axis at (negative 2 omma 0) and moves to quadrant 3 through the point (negative 2 point 5 comma negative 10).

Image with description On a coordinate plane with x and y axes marked from negative 10 to 10, a polynomial graph is drawn. It starts from quadrant 4, passes through (negative 3 point 2 comma negative 10), touches x axis at (negative 2 comma 0), moves down and crosses y axis at (0 comma negative 0). It moves down and curves up at (0 point 5 comma negative 9 point 5), passes through the x axis at (2 comma 0) and moves to quadrant 1 through (2 point 5 comma 10).

Image with description On a coordinate plane with x and y axes marked from negative 10 to 10, a polynomial graph is drawn. It starts from quadrant 2, passes through(negative 5 comma 10), touches the x axis at (negative 2 comma 0), passes through the y axis at (0 comma 4), and moves to quadrant 1 through (1 comma 10).

Explanation

For f(x) = x³ + 8, the y-intercept is f(0) = 8, and the x-intercept satisfies x³ + 8 = 0, so x = −2. The function is an increasing cubic, with values such as f(1) = 9 and f(−2.5) ≈ −7.6, which match the points described in choice B. Choice A has its x-intercept at 2, while the other choices do not match the intercepts and shape.

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