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ConstructingFunctions Express the gross salary G of a person who earns $10 per hour as a function of the number x of hours worked.

How many x-intercepts can a function defined on an interval have if it is increasing on that interval? Explain.

The graph of a function f is illustrated in the figure.

1. Draw the graph of $y=\left|f\left(x\right)\right|$
2. Draw the graph of$y=f\left(\left|x\right|\right)$

Suppose that a friend of yours does not understand the idea of increasing and decreasing functions. Provide an explanation, complete with graphs, that clarifies the idea.

Constructing Functions Tiffany, a commissioned sales person, earns \(100 base pay plus \)10 per item sold. Express her gross salary G as a function of the number x of items sold.

Suppose $\left(1,3\right)$is a point on the graph of $y=f\left(x\right)$.

(a) What point is on the graph of$y=f(x+3)-5$?

(b) What point is on the graph of $y=-2f\left(x-2\right)+1$?

(c) What point is on the graph of $y=\left(2x+3\right)$?

Can a function be both even and odd? Explain.

Suppose $\left(-3,5\right)$is a point on the graph of role="math" localid="1646038713489" $y=g\left(x\right)$.

(a) What point is on the graph of role="math" localid="1646038862365" $y=g(x+1)-3$?

(b) What point is on the graph of $y=-3g\left(x-4\right)+3$?

(c) What point is on the graph of$y=g\left(3x+9\right)$?

Population as a Function of Age The function

$P\left(a\right)=0.015a^2-4.962a+290.580$

represents the population P (in millions) of Americans that are a years of age or older.

(a) Identify the dependent and independent variables.

(b) Evaluate $P\left(20\right)$. Provide a verbal explanation of the meaning of $P\left(20\right)$.

(c) Evaluate $P\left(0\right)$. Provide a verbal explanation of the meaning of $P\left(0\right)$.

Using a graphing utility, graph y = 5 on the interval (-3, 3). Use MAXIMUM to find the local maximum values on (-3, 3).