Question

use the select power slider to graph the power function $f(x)=x^{2}$. use the graph to answer parts 1 through 5 below. use the interactive figure to find your answer. use the left and right arrow keys to move along a slider as needed. click here to launch the interactive figure. part 1: $f(2)=4$ (simplify your answer.) part 2: $f(-2)=4$ (simplify your answer.) part 3: $f(1)=1$ (simplify your answer.) part 4: $f(\frac{1}{2})=\frac{1}{4}$ (simplify your answer.) part 5: check the $y = x$ box and the zoom in selector. is it true or false that if $x>0$, then $f(x)>x$? true false

Explanation:

Step1: Analyze the function \(f(x)=x^{2}\)

Given the function \(f(x) = x^{2}\), for \(x>0\), we need to check if \(x^{2}>x\).

Step2: Solve the inequality \(x^{2}-x>0\)

Factor the left - hand side: \(x(x - 1)>0\). The critical points are \(x = 0\) and \(x=1\).
For \(0\frac{1}{4}\) (since \(\frac{1}{2}=0.5\) and \(\frac{1}{4}=0.25\)).
For \(x>1\), let \(x = 2\). Then \(f(2)=4\) and \(4>2\).

Answer:

False