# 2.1 Linear functions  (Page 9/17)

 Page 9 / 17

## Verbal

Terry is skiing down a steep hill. Terry's elevation, $E\left(t\right),$ in feet after $t$ seconds is given by $E\left(t\right)=3000-70t.$ Write a complete sentence describing Terry’s starting elevation and how it is changing over time.

Terry starts at an elevation of 3000 feet and descends 70 feet per second.

Maria is climbing a mountain. Maria's elevation, $E\left(t\right),$ in feet after $t$ minutes is given by $E\left(t\right)=1200+40t.$ Write a complete sentence describing Maria’s starting elevation and how it is changing over time.

Jessica is walking home from a friend’s house. After 2 minutes she is 1.4 miles from home. Twelve minutes after leaving, she is 0.9 miles from home. What is her rate in miles per hour?

3 miles per hour

Sonya is currently 10 miles from home and is walking farther away at 2 miles per hour. Write an equation for her distance from home t hours from now.

A boat is 100 miles away from the marina, sailing directly toward it at 10 miles per hour. Write an equation for the distance of the boat from the marina after t hours.

$d\left(t\right)=100-10t$

Timmy goes to the fair with $40. Each ride costs$2. How much money will he have left after riding $n$ rides?

## Algebraic

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$y=\frac{1}{4}x+6$

Yes.

$y=3x-5$

$y=3{x}^{2}-2$

No.

$3x+5y=15$

$3{x}^{2}+5y=15$

No.

$3x+5{y}^{2}=15$

$-2{x}^{2}+3{y}^{2}=6$

No.

$-\frac{x-3}{5}=2y$

For the following exercises, determine whether each function is increasing or decreasing.

$f\left(x\right)=4x+3$

Increasing.

$g\left(x\right)=5x+6$

$a\left(x\right)=5-2x$

Decreasing.

$b\left(x\right)=8-3x$

$h\left(x\right)=-2x+4$

Decreasing.

$k\left(x\right)=-4x+1$

$j\left(x\right)=\frac{1}{2}x-3$

Increasing.

$p\left(x\right)=\frac{1}{4}x-5$

$n\left(x\right)=-\frac{1}{3}x-2$

Decreasing.

$m\left(x\right)=-\frac{3}{8}x+3$

For the following exercises, find the slope of the line that passes through the two given points.

and

3

and

$\left(-1,\text{4}\right)$ and $\left(5,\text{2}\right)$

$–\frac{1}{3}$

$\left(8,-2\right)$ and $\left(4,6\right)$

and

$\frac{4}{5}$

For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

$f\left(-5\right)=-4,$ and $f\left(5\right)=2$

$f\left(-1\right)=4$ and $f\left(5\right)=1$

$f\left(x\right)=-\frac{1}{2}x+\frac{7}{2}$

$\left(2,4\right)$ and $\left(4,10\right)$

Passes through $\left(1,5\right)$ and $\left(4,11\right)$

$y=2x+3$

Passes through and

Passes through and

$y=-\frac{1}{3}x+\frac{22}{3}$

x intercept at and y intercept at $\left(0,-3\right)$

x intercept at and y intercept at

$y=\frac{4}{5}x+4$

## Graphical

For the following exercises, find the slope of the lines graphed.  $-\frac{5}{4}$ For the following exercises, write an equation for the lines graphed. $y=\frac{2}{3}x+1$  $y=-2x+3$  $y=3$ ## Numeric

For the following exercises, which of the tables could represent a linear function? For each that could be linear, find a linear equation that models the data.

 $x$ 0 5 10 15 $g\left(x\right)$ 5 –10 –25 –40

Linear, $g\left(x\right)=-3x+5$

 $x$ 0 5 10 15 $h\left(x\right)$ 5 30 105 230
 $x$ 0 5 10 15 $f\left(x\right)$ –5 20 45 70

Linear, $f\left(x\right)=5x-5$

 $x$ 5 10 20 25 $k\left(x\right)$ 28 13 58 73
 $x$ 0 2 4 6 $g\left(x\right)$ 6 –19 –44 –69

Linear, $g\left(x\right)=-\frac{25}{2}x+6$

 $x$ 2 4 6 8 $f\left(x\right)$ –4 16 36 56
 $x$ 2 4 6 8 $f\left(x\right)$ –4 16 36 56

Linear, $f\left(x\right)=10x-24$

 $x$ 0 2 6 8 $k\left(x\right)$ 6 31 106 231

## Technology

If $f$ is a linear function, find an equation for the function.

$f\left(x\right)=-58x+17.3$

Graph the function $f$ on a domain of Enter the function in a graphing utility. For the viewing window, set the minimum value of $x$ to be $-10$ and the maximum value of $x$ to be $10.$

Graph the function $f$ on a domain of what is the importance knowing the graph of circular functions?
can get some help basic precalculus
What do you need help with?
Andrew
how to convert general to standard form with not perfect trinomial
can get some help inverse function
ismail
Rectangle coordinate
how to find for x
it depends on the equation
Robert
whats a domain
The domain of a function is the set of all input on which the function is defined. For example all real numbers are the Domain of any Polynomial function.
Spiro
foci (–7,–17) and (–7,17), the absolute value of the differenceof the distances of any point from the foci is 24.
difference between calculus and pre calculus?
give me an example of a problem so that I can practice answering
x³+y³+z³=42
Robert
dont forget the cube in each variable ;)
Robert
of she solves that, well ... then she has a lot of computational force under her command ....
Walter
what is a function?
I want to learn about the law of exponent
explain this
what is functions?
A mathematical relation such that every input has only one out.
Spiro
yes..it is a relationo of orders pairs of sets one or more input that leads to a exactly one output.
Mubita
Is a rule that assigns to each element X in a set A exactly one element, called F(x), in a set B.
RichieRich
If the plane intersects the cone (either above or below) horizontally, what figure will be created?
can you not take the square root of a negative number
No because a negative times a negative is a positive. No matter what you do you can never multiply the same number by itself and end with a negative
lurverkitten
Actually you can. you get what's called an Imaginary number denoted by i which is represented on the complex plane. The reply above would be correct if we were still confined to the "real" number line.
Liam By By By OpenStax By OpenStax By Madison Christian By Nicole Duquette By Robert Murphy By Brooke Delaney By OpenStax By OpenStax By Katy Pratt By Brooke Delaney