91Ó°ÊÓ

In Problems $39-68$, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, $y=x^2$) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.Verify your results using a graphing utility.

$g\left(x\right)=2\sqrt{x-2}+1$

In Problems 47– 62, find the domain of each function.

$p\left(x\right)=\sqrt{\frac{2}{x-1}}$

Find the domain of each function.

$f\left(x\right)=\frac{x}{x^2-9}$

Use a graphing utility to graph the function $f\left(x\right)=-x^4+2x^3+4x^2-2$on the interval $(-5,5)$. Approximate any local maximum values and local minimum values rounded to two decimal places. Determine where the function is increasing and where it is decreasing.

Find the real solutions of the equation:

$\sqrt{2x+3}=2$

The set of all images of the elements in the domain of a function is called the _________.

True or False The cube function is odd and is increasing on the interval $(-∞,∞)$.

True or False

To obtain the graph of $f\left(x\right)=x^3+5,$shift the graph of $y=x^3$vertically up $5$units.

A right triangle has one vertex on the graph of $y=9-x^2,x>0$, at $\left(x,y\right)$, another at the origin, and the third on the positive x-axis at $\left(x,0\right)$. Express the area Aof the triangle as a function of x.

Concepts and Vocabulary

A function f is ___________ on an open interval I if, for any choice of x1 and x2 in I, with$x_1<x_{2}wehavef\left(x_1\right)<f\left(x_2\right)$