MathTV Topic - Linear & Exponential Functions

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Math Topics

Quantitative Literacy
Linear & Exponential Functions

1
Introduction to Functions

Problem 1

Determine the domain and range of the relations shown.

Choose instructor to watch:

Mr. McKeague

Molly S.

Logan

Cynthia

Problem 2

Determine whether each given relation is a function.

Choose instructor to watch:

Mr. Perez

Julieta

Problem 3

Determine whether each given relation is a function.

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Mr. Perez

Julieta

Problem 4

Determine whether each equation is a function.

$3x-2y=6$
$y=7$
$x=3$
$y=\dfrac{1}{2}x-1$

Choose instructor to watch:

Mr. Perez

Julieta

Problem 5

Is $f(x)=4x-1$ and $g(x)=x^2+2$, then find $f(x)$ and $g(x)$ when $x=5$, $-2$, $0$, $z$, $a$, and $a+3$.

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Betsy

Preston

Julieta

Problem 6

$f=\{(-2,0), (3,-1), (2,4), (7,5)\}$ find $f(-2)$, $f(3)$, $f(2)$, and $f(7)$

Choose instructor to watch:

Betsy

Preston

Edwin

Problem 7

Mini Lecture
Let $f(x)=2x-1$ and $g(x)=x^2-4$ find

a. $f(0)$	$\quad$ b. $f(1)$	$\quad$ c. $f(-1)$
d. $f(a)$	$\quad$ e. $g(0)$	$\quad$ f. $g(-2)$
g. $g(3)$	$\quad$ h. $g(t)$	$\quad$ i. $f(a+5)$
j. $f(x+h)$	$\quad$ k. $g(a-1)$	$\quad$ l. $g(f(x))$

Choose instructor to watch:

Mr. McKeague

Mini Lecture

Mini Lecture
Let $f(x)=2x^2-8$, find:

$f(0)$
$f(-3)$
$f(a)$
$f(a-3)$
Graph $f(x)=x^2$ and find $f(1)$, $f(2)$, and $f(3)$.

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Mr. McKeague

Problem 9

Mini Lecture
Let $f(x)=2x-1$ and $g(x)=x^2-4$ find

Find $x$ if $f(x)=0$
Find $x$ if $g(x)=0$
Find $x$ if $f(x)=g(x)$

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Mr. McKeague

Mini Lecture

Mini Lecture
Are these functions?

$\{(7,-1), (3,-1), (7,4)\}$
$\{(4,1), (1,4), (-1,-4)\}$

Choose instructor to watch:

Mr. McKeague

2
Slope

Problem 1

Find the slope through $(1, 2)$ and $(3, 5)$

Choose instructor to watch:

Betsy

Preston

Katherine

David

Problem 2

Find the slope through $(-2,1)$ and $(5, -4)$

Choose instructor to watch:

Betsy

Preston

Molly S.

Cynthia

Problem 3

Find the slope of the line containing $(3,-1)$ and $(3,4)$.

Choose instructor to watch:

Betsy

Preston

Cynthia

Problem 4

Graph the line with slope $\dfrac{3}{2}$ and $y$-intercept $1$.

Choose instructor to watch:

Betsy

Preston

Molly S.

Cynthia

Problem 5

Find the slope and $y$-intercept for $-2x+y=-4$. Then draw the graph.

Choose instructor to watch:

Betsy

Preston

Cynthia

Problem 6

Find the slope and $y$-intercept for $3x-2y=6$.

Choose instructor to watch:

Betsy

Preston

Cynthia

Problem 7

Determine whether each pair of lines is parallel, perpendicular, or neither.

\[\begin{aligned} y &= \dfrac{1}{4}x-5\\ 4x+y &= 3\end{aligned}\]
\[\begin{aligned} 3x+2y &= 6\\ 6x+4y &= 0\end{aligned}\]
\[\begin{aligned} 2x+y &= 1\\ x-3y &= 6\end{aligned}\]

Choose instructor to watch:

Julieta

Mini Lecture

Mini Lecture

Find the slope between $(-3,-2)$ and $(1,3)$.
Graph the line with the slope $\displaystyle\frac{3}{2}$ and $y$-intercept $-3$.

Choose instructor to watch:

Mr. McKeague

3
Linear Regression

Problem 1

Choose instructor to watch:

Molly S.

Octabio

Julieta

Problem 2

Choose instructor to watch:

Kendra

Logan

Julieta

Problem 3

Choose instructor to watch:

Logan

Molly S.

Cynthia

Octabio

Problem 4

Choose instructor to watch:

Kendra

Logan

Mini Lecture

Choose instructor to watch:

Katherine

4
Exponential Functions and Applications

Problem 1

Find the values of the exponential functions $f$ and $g$, where $f(x)=2^x$ and $g(x)=3^x$, and $x\in \{0,1,2,3,-2,-3\}$.

Choose instructor to watch:

Stefanie

Preston

Anthony

Problem 2

A patient is administered a $1200$-microgram dose of iodine-$131$. How much iodine-$131$ will be in the patientâ€™s system after $10$ days, after $16$ days?

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Stefanie

Edwin

Problem 3

Sketch the graph of the exponential equation $y=2^x$

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Jesse

Betsy

Preston

Julieta

Problem 4

Sketch the graph of $y=\left( \displaystyle\frac{1}{3} \right) ^x$

Choose instructor to watch:

Betsy

Edwin

Problem 5

You deposit $\$500$ in an account that earns $8\%$ compounded quarterly. Find an equation that gives the amount of money in the account after $t$ years, the amount in the account after $5$ years, and when it will contain $\$1\text{,}000$.

Choose instructor to watch:

Stefanie

Preston

Anthony

Problem 6

You deposit $\$500$ in an account with an annual interest rate of $8\%$ compounded continuously. Find an equation that gives the amount of money in the account after $t$ years, the amount in the account after $5$ years.

Choose instructor to watch:

Stefanie

Edwin

Mini Lecture

Mini Lecture
If $f(x)=3^x$ and $g(x)=\left(\displaystyle\frac{1}{2}\right)^x$, find:

$g(0)$
$f(-3)$
$f(2)+g(-2)$
Graph $y=2^x$
Graph $y=3^x$ and its inverse.

Choose instructor to watch:

Mr. McKeague

5
Algebraic Expressions

Problem 1

Simplify.

$3x+4x$
$7a-10a$
$18y-10y+6y$

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Arielle

Molly M.

Preston

David

Problem 2

Simplify.

$3x+5+2x-3$
$4a-7-2a+4$
$5x+8-x+6$

Choose instructor to watch:

Arielle

Molly M.

David

Problem 3

Simplify $5(2x-8)-3$

Choose instructor to watch:

Arielle

Molly M.

Preston

David

Problem 4

Simplify $7-3(2y+1)$

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Stefanie

Arielle

David

Problem 5

Simplify $5(x-2)-(3x+4)$

Choose instructor to watch:

Arielle

Molly M.

Preston

David

Problem 6

Find the value of the expression $2x-3y+4$ when $x$ is $-5$ and $y$ is $6$.

Choose instructor to watch:

Arielle

Molly M.

Preston

David

Problem 7

Find the value of the expression $3x^2y$ when $x=-2$ and $y=4$.

Choose instructor to watch:

Julieta

Problem 8

Find the value of the expression $x^2-2xy+y^2$ when $x$ is $3$ and $y$ is $-4$.

Choose instructor to watch:

Arielle

Molly M.

David

Problem 9

Translate each word phrase into an algebraic expression.

seven added to three times a number $x$
the product of $4x$ and $y$
four less than twice $x$

Choose instructor to watch:

Julieta

Problem 10

Mini Lecture
Solve.

$x+2=6$
$-\displaystyle\frac{5}{9}=x-\displaystyle\frac{2}{5}$
$4x+2-3x=4+1$
$4y-3(y-6)+2=8$
$8a=7a-5$

Choose instructor to watch:

Mr. McKeague

6
Linear Equations in One Variable

Problem 1

Solve: $3(x+2)=-9$

Choose instructor to watch:

Mr. McKeague

Julieta

Problem 2

Solve: $4a+5=2a-7$

Choose instructor to watch:

Mr. McKeague

Katrina

Julieta

David

Problem 3

Solve: $2(x-4)+5=-11$

Choose instructor to watch:

Mr. McKeague

Logan

Arielle

David

Problem 4

Solve: $5(2x-4)+3=4x-5$

Choose instructor to watch:

Mr. McKeague

Julieta

Arielle

David

Problem 5

Solve: $\displaystyle\frac{x}{2}+\displaystyle\frac{x}{6}=8$

Choose instructor to watch:

Mr. McKeague

Matt

Arielle

David

Problem 6

Solve: $2x+\displaystyle\frac{1}{2}=\displaystyle\frac{3}{4}$

Choose instructor to watch:

Mr. McKeague

Anthony

Arielle

David

Problem 7

Solve: $\displaystyle\frac{3}{x}+2=\displaystyle\frac{1}{2}$

Choose instructor to watch:

Mr. McKeague

Katrina

Matt

David

Problem 8

Mini Lecture
Solve.

$6(x-3)=-6$
$7y-3=4y-15$
$2(3x-6)+1=7$
$9x-6=-3(x+2)-24$
$\dfrac{x}{5}-x=4$
$\dfrac{1}{x}-\dfrac{1}{2}=-\dfrac{1}{4}$

Choose instructor to watch:

Mr. McKeague

7
Evaluating Formulas

Problem 1

Find the area and perimeter of a square with a side $6$ inches long.

Choose instructor to watch:

Mr. McKeague

Julieta

Mrs. Mooney

Anthony

Problem 2

The perimieter $P$ of a rectangular livestock pen is $40$ feet. If the width $w$ is $6$ feet, find the length.

Choose instructor to watch:

Mr. McKeague

Julieta

Aaron

Julieta

Problem 3

Use the formula $C=\dfrac{5(F-32)}{9}$ to find $C$ when $F$ is $95$ degrees.

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Mr. McKeague

Winston

Octabio

Problem 4

Use the formula $y=2x+6$ to find $y$ when $x$ is $-2$

Choose instructor to watch:

Mr. McKeague

Lauren

Aaron

Julieta

Problem 5

Find $y$ when $x$ is $3$ in the formula $2x+3y=4$

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Mr. McKeague

Aaron

David

Problem 6

At $1$ P.M. Jordan leaves her house and drives an average speed of $50$ miles per hour to her sisterâ€™s house. She arrives at $4$ P.M.

How many hours was the drive to her sisterâ€™s house?
How many miles from her sister does Jordan live?

Choose instructor to watch:

Katrina

Aaron

Julieta

Problem 7

Find the complement and supplement of $25^\circ$

Choose instructor to watch:

Arielle

Aaron

David

Problem 8

Mini Lecture
Let $G=H\cdot R$ and find $G$, if

$H=36$ hours and $R=\$8$ per hour.
$H=20$ hours and $R=\$6\frac{3}{4}$ per hour.

If $C=\dfrac{5}{9}(F-32)$, find $C$ if

$F=158$
$F=32$

If $A=\pi r^2$, find $A$ if $\pi=\dfrac{22}{7}$ and

$r=7$ feet
$r=\dfrac{3}{4}$ feet

Choose instructor to watch:

Mr. McKeague

8
Test & Summary

No examples are currently assigned to this topic.

a. \(f(0)\)	\(\quad\) b. \(f(1)\)	\(\quad\) c. \(f(-1)\)
d. \(f(a)\)	\(\quad\) e. \(g(0)\)	\(\quad\) f. \(g(-2)\)
g. \(g(3)\)	\(\quad\) h. \(g(t)\)	\(\quad\) i. \(f(a+5)\)
j. \(f(x+h)\)	\(\quad\) k. \(g(a-1)\)	\(\quad\) l. \(g(f(x))\)

CHOOSE A TOPIC

1 Introduction to Functions

2 Slope

3 Linear Regression

4 Exponential Functions and Applications

5 Algebraic Expressions

6 Linear Equations in One Variable

7 Evaluating Formulas

8 Test & Summary

1
Introduction to Functions

2
Slope

3
Linear Regression

4
Exponential Functions and Applications

5
Algebraic Expressions

6
Linear Equations in One Variable

7
Evaluating Formulas

8
Test & Summary