Question

answer the following questions.

1. choose the correct equation or inequality by using the indicated points.

graph with points (0,0), (1,1), (4,2) and function options: f(x)=x², f(x)=x, f(x)=x^(1/2), f(x)=∛x

Explanation:

Step1: Test \( f(x)=x^2 \)

Substitute \( x = 1 \): \( f(1)=1^2 = 1 \) (matches (1,1)), \( x = 4 \): \( f(4)=4^2 = 16
eq 2 \) (does not match (4,2)).

Step2: Test \( f(x)=x \)

Substitute \( x = 4 \): \( f(4)=4
eq 2 \) (does not match (4,2)).

Step3: Test \( f(x)=x^{\frac{1}{2}} \)

\( x^{\frac{1}{2}}=\sqrt{x} \). Substitute \( x = 1 \): \( \sqrt{1}=1 \) (matches (1,1)), \( x = 4 \): \( \sqrt{4}=2 \) (matches (4,2)), \( x = 0 \): \( \sqrt{0}=0 \) (matches (0,0)).

Step4: Test \( f(x)=\sqrt[3]{x} \)

Substitute \( x = 4 \): \( \sqrt[3]{4}\approx1.59
eq2 \) (does not match (4,2)).

Answer:

\( f(x)=x^{\frac{1}{2}} \)