Expressions, Equations, and Functions

Determine whether each relation is a function. Explain.

Examples 1 and 3 Determine whether each relation is a function. Explain.

Determine whether each relation is a function. Explain.

Examples 1 and 3 Determine whether each relation is a function. Explain.

SCHOOL ENROLLMENT The table shows the total enrollment in U.S. public schools.

b. Draw a graph showing the relationship between the year and enrollment.

c. Describe the domain and range of the data.

CELL PHONES The cost of sending cell phone pictures is given by $y=0.25x$ where $x$ is the number of pictures that you send. Write the equation in function notation and then find $f\left(5\right)$ and $f\left(12\right)$. What do these values represent? Determine the domain and range of this function.

Examples 4 and 5 If $f\left(x\right)=6x+7$ and $g\left(x\right)=x^2-4,$ find each value. (P. 49)

$f(-3)$

Examples 4 and 5 If $f\left(x\right)=6x+7$ and $g\left(x\right)=x^2-4,$ find each value. (P. 49)

$f\left(m\right)$

Examples 4 and 5 If $f\left(x\right)=6x+7$ and $g\left(x\right)=x^2-4,$ find each value. (P. 49)

 $f(r-2)$

Examples 4 and 5 If $f\left(x\right)=6x+7$ and $g\left(x\right)=x^2-4,$ find each value. (P. 49)

$g\left(5\right)$

Examples 4 and 5 If $f\left(x\right)=6x+7$ and $f\left(x\right)=6x+7$ find each value. (P. 49)

$g\left(a\right)+9$

Examples 4 and 5 If $f\left(x\right)=6x+7$ and $g\left(x\right)=x^2-4,$ find each value. (P. 49)

$g(-4t)$

Examples 4 and 5 If $f\left(x\right)=6x+7$ and $g\left(x\right)=x^2-4,$ find each value. (P. 49)

$f(q+1)$

Examples 4 and 5 If $f\left(x\right)=6x+7$ and $g\left(x\right)=x^2-4,$ find each value. (P. 49)

$f\left(2\right)+g(-2)$

Examples 4 and 5 If $f\left(x\right)=6x+7$ and $g\left(x\right)=x^2-4,$ find each value. (P. 49)

$g(-b)$

Example 1 Determine whether each relation is a function. Explain.

Determine whether each relation is a function. Explain.

Example 1 Determine whether each relation is a function. Explain

Determine whether each relation is a function. Explain.

Example 1 Determine whether each relation is a function. Explain.

Determine whether each relation is a function. Explain.

HOME VALUE The table shows the median home prices in Raleigh, North Carolina,

a. Write a set of ordered pairs representing the data in the table.

b. Draw a graph showing the relationship between the year and price.

c. What is the domain and range for this data?

Example 3 Determine whether each relation is a function.

$\left[\right(5,-7),(6,-7),(-8,-1),(0,-1\left)\right\}$

Determine whether each relation is a function.

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

Example 3 Determine whether each relation is a function.

$y=-8$

Example 3 Determine whether each relation is a function.

$x=15$

Example 3 Determine whether each relation is a function.

$y=3x-2$

Determine whether each relation is a function.

$y=3x+2y$

Examples 4 and 5 If $f\left(x\right)=-2x-3$ and $g\left(x\right)=x^2+5x,$ find each value. (P. 50)

$f(-1)$

Examples 4 and 5 If $f\left(x\right)=-2x-3$ and $g\left(x\right)=x^2+5x,$ find each value. (P. 50)

$f\left(6\right)$

Examples 4 and 5 If $f\left(x\right)=-2x-3$ and $g\left(x\right)=x^2+5x,$ find each value. (P. 50)

$g\left(2\right)$

Examples 4 and 5 If $f\left(x\right)=-2x-3$ and $g\left(x\right)=x^2+5x,$ find each value.

$g(-3)$

 If $g\left(x\right)=x^2+5x,$ find the value of $g(-2)$.

Examples 4 and 5 If $f\left(x\right)=-2x-3$ and $g\left(x\right)=x^2+5x,$ find each value. (P. 50)

$f\left(0\right)-7$

Examples 4 and 5 If $f\left(x\right)=-2x-3$ and $g\left(x\right)=x^2+5x,$ find each value. (P. 50)

$f\left(4y\right)$

Examples 4 and 5 If $f\left(x\right)=-2x-3$ and $g\left(x\right)=x^2+5x,$ find each value. (P. 50)

$g(-6m)$

Examples 4 and 5 If $f\left(x\right)=-2x-3$ and $g\left(x\right)=x^2+5x,$ find each value. (P. 50)

$f(c-5)$

Examples 4 and 5 If $f\left(x\right)=-2x-3$ and $g\left(x\right)=x^2+5x,$ find each value. (P. 50)

$f(r+2)$

Examples 4 and 5 If $f\left(x\right)=-2x-3$ and $g\left(x\right)=x^2+5x,$ find each value. (P. 50)

$5\left[f\right(d\left)\right]$

Examples 4 and 5 If $f\left(x\right)=-2x-3$ and $g\left(x\right)=x^2+5x,$ find each value. (P. 50)

$3\left[g\right(n\left)\right]$

EDUCATION The average national math test scores $f\left(t\right)$ for 17-year-olds can be represented as a function of the national science scores $t$ by $f\left(t\right)=0.8t+72$.

a. Graph this function.

b. What is the science score that corresponds to a math score of 308 ?

c. What is the domain and range of this function?

Determine whether each relation is a function.

Determine whether each relation is a function.

BABYSITTING Christina earns $ 7.50 an hour babysitting.

a. Write an algebraic expression to represent the money Christina will earn if she works $h$ hours.

b. Choose five values for the number of hours Christina can babysit. Create a table with $h$ and the amount of money she will make during that time.

c. Use the values in your table to create a graph.

d. Does it make sense to connect the points in your graph with a line? Why or why not?

The set of ordered pairs $\left\{(0,1),(3,2),(3,-5),(5,4)\right\}$ represents a relation between x and y. Graph the set of ordered pairs. Determine whether the relation is a function. Explain.

CHALLENGE Consider $f\left(x\right)=–4.3x–2$ Writing $f(g+3.5)$ and simplifying by combining like terms.

WRITE A QUESTION A classmate graphed a set of ordered pairs and used the vertical line test to determine whether it was a function. Write a question to help her decide if the same strategy can be applied to mapping.

If $f(3b-1)=9b-1,$ find one possible expression for f(x).

FIND THE ERROR Corazon and Maggie are analyzing the relation to determine whether it is a function. Is either of them correct? Explain your reasoning.

WRITING IN MATH Use the graph of stopping distances on page 45 to explain how graphs and functions can be used to model real-world situations.