91Ó°ÊÓ

Suppose that the graph of a function f is known. Then the graph of $y=f(x-2)$may be obtained by a(n) ________ shift of the graph of $f$ to the ________ a distance of$2$ units.

The interval (2, 5) can be written as the inequality ___________

The inequality$-1<x<3$can be written in interval notation as___________.

Determine whether each relation represents a function.For each function, State the domain and the range.

(a) $\left\{\right(2,5),(4,6),(6,7),(8,8\left)\right\}$

(b) $\left\{\right(1,3),(4,-2),(-3,5),(1,7\left)\right\}$

(c)

(d)

Use the given graph of the function f to answer parts (a) – (n).

(a) Find $f\left(0\right)$ and $f\left(6\right)$.

(b) Find $f\left(2\right)$and $f\left(-2\right)$.

(c) Is $f\left(3\right)$positive or negative?

(d) Is $f\left(-1\right)$positive or negative?

(e) For what values of x is $f\left(x\right)=0$?

(f) For what values of x is localid="1650172833683" $f\left(x\right)<0$?

(g) What is the domain of f ?

(h) What is the range of f ?

(i) What are the x-intercepts?

(j) What is the y-intercept?

(k) How often does the line y = -1 intersect the graph?

(l) How often does the line x = 1 intersect the graph?

(m) For what value of x does $f\left(x\right)=3$?

(n) For what value of x does $f\left(x\right)=-2$?

True or False Every relation is a function.

A circle of radius ris in inscribed in a square. See the figure.

Part (a): Express the area A of the square as a function of the radius rof the circle.

Part (b): Express the perimeter p of the square as a function of the radius rof the circle.

Match each graph to its function.

A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function H. Cube root function

Profit Function Suppose that the revenue $R$, in dollars, from selling x clocks is $R\left(x\right)=30x$. The cost $C$, in dollars, of selling x clocks is $C\left(x\right)=0.1x^2+7x+400$.

(a) Find the profit function, $P\left(x\right)=R\left(x\right)-C\left(x\right)$.

(b) Find the profit if $x=30$clocks are sold.

(c) Interpret $P\left(30\right)$.

A wire $10$meters long is to be cut into two pieces. One piece will be shaped as a square, and the other piece will be shaped as a circle. See the figure.

Part (a): Express the total area Aenclosed by the pieces of wire as a function of the length x of a side of the square.

Part (b): What is the domain of A?

Part (c): Graph $A=A\left(x\right)$. For what value of xis Asmallest?