2.1 Linear functions  (Page 9/17)

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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

Questions & Answers

difference between calculus and pre calculus?
Asma Reply
give me an example of a problem so that I can practice answering
Jenefa Reply
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?
CJ Reply
I want to learn about the law of exponent
Quera Reply
explain this
Hinderson Reply
what is functions?
Angel Reply
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?
Feemark Reply
can you not take the square root of a negative number
Sharon Reply
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
Suppose P= {-3,1,3} Q={-3,-2-1} and R= {-2,2,3}.what is the intersection
Elaine Reply
can I get some pretty basic questions
Ama Reply
In what way does set notation relate to function notation
Ama
is precalculus needed to take caculus
Amara Reply
It depends on what you already know. Just test yourself with some precalculus questions. If you find them easy, you're good to go.
Spiro
the solution doesn't seem right for this problem
Mars Reply
what is the domain of f(x)=x-4/x^2-2x-15 then
Conney Reply
x is different from -5&3
Seid
All real x except 5 and - 3
Spiro
***youtu.be/ESxOXfh2Poc
Loree
how to prroved cos⁴x-sin⁴x= cos²x-sin²x are equal
jeric Reply
Don't think that you can.
Elliott
By using some imaginary no.
Tanmay
how do you provided cos⁴x-sin⁴x = cos²x-sin²x are equal
jeric Reply
What are the question marks for?
Elliott

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