Match the graph with its function using the x-intercepts.
-$y = x ^ { 2 / 3 } + 4 x ^ { 1 / 3 }$ and $y = 5$
A) $- 125,1$
B) $- 5,1$
C) $- 1,5$
D) $- 1,125$

Question

Quizplus · Accepted Answer

The x-intercepts of the function $y = x^{2/3} + 4x^{1/3}$ are found by setting the function equal to zero: $x^{2/3} + 4x^{1/3} = 0$. Solving this gives $x^{1/3}(x^{1/3} + 4) = 0$, leading to $x^{1/3} = 0$ or $x^{1/3} = -4$. Thus, $x = 0$ or $x = -64$. The x-intercepts of the line $y = 5$ are not relevant here. The closest match to these intercepts is option A, which includes $-125$ as a potential x-intercept.

Match the Graph with Its Function Using the X-Intercepts y=x2/3+4x1/3y = x ^ { 2 / 3 } + 4 x ^ { 1 / 3 }y=x2/3+4x1/3

Match the Graph with Its Function Using the X-Intercepts $y = x ^ { 2 / 3 } + 4 x ^ { 1 / 3 }$