Question

the graph of $p(x)=\frac{1}{3}\sqrt3{x}-1$ has -
a one x-intercept and one y-intercept
b one x-intercept and no y-intercept
c two x-intercepts and one y-intercept
d no x-intercept and one y-intercept

Explanation:

Step1: Find x-intercept (set $p(x)=0$)

Set $\frac{1}{3}\sqrt[3]{x} - 1 = 0$

Step2: Isolate the cube root term

$\frac{1}{3}\sqrt[3]{x} = 1$

Step3: Solve for $\sqrt[3]{x}$

$\sqrt[3]{x} = 3$

Step4: Solve for x

$x = 3^3 = 27$

Step5: Find y-intercept (set $x=0$)

$p(0)=\frac{1}{3}\sqrt[3]{0} - 1 = -1$

Answer:

A. one x-intercept and one y-intercept