Determining if Linear
Determine if the function \( f(x) = 3x + 5 \) is linear.
Rewriting as an Equation
If the function \( f(x) = 2x + 3 \), find the equation of the function when \( f(x) = 5 \).
Rewriting as y=mx+b
Rewrite the equation \(3x - 2y = 6\) in the form \(y = mx + b\)
Solving Function Systems
Solve the following system of functions: \(f(x) = 3x + 2\) and \(g(x) = 2x - 1\).
Find the Behavior (Leading Coefficient Test)
For the function $y=(x-8)(x+2)$, its $y$-intercept is
its $x$-intercepts are $x=$
Note: If there is more than one $x$-intercept write the $\mathrm{x}$-values separated by commmas.
When $x \rightarrow \infty, y \rightarrow$
$\infty$ (Input + or - for the answer)
When $x \rightarrow-\infty, y \rightarrow$ $\infty$ (Input + or - for the answer)
Determining Odd and Even Functions
Determine whether the function \(f(x) = x^3 + 2x\) is odd, even, or neither.
Finding the Antiderivative
on $f(x)=\frac{x}{3}+10$, find $f^{-1}(x)$
Describing the Transformation
5. Suppose that the graph of the function $f(x)=2 x^{2}$ is reflected in the $x$-axis, translated 2 units to the left, and then translated 5 units upward. What could the equation of the quadratic function of the resultant graph be?
A. $f(x)=-(x+2)^{2}+5$
B. $f(x)=2(-x-2)^{2}+5$
C. $f(x)=-2(x-2)^{2}+5$
D. $f(x)=-2(x+2)^{2}+5$
Graphing
Given the piecewise function
\[
f(x)=\left\{\begin{array}{lll}
x & \text { if } & x<2 \\
-x+4 & \text { if } & x \geq 2
\end{array}\right.
\]
Graph the function.
Note: Be sure to include closed or open dots, but only at breaks in the graph.
Arrows are assumed if no end symbols are shown.
Finding the Symmetry
Determine whether the function f(x) = x^3 - 3x is odd, even, or neither.
Arithmetic of Functions
Evaluate the function $h(x)=x^{4}-4 x^{2}+5$ at the given values of the independent variable and simplify.
a. $h(-2)$
b. $h(-1)$
c. $h(-x)$
d. $h(3 a)$
a. $h(-2)=5$ (Simplify your answer.)
b. $h(-1)=\square$ (Simplify your answer.)
c. $h(-x)=\square$ (Simplify your answer.)
d. $h(3 a)=\square$ (Simplify your answer. $)$
Finding Roots Using the Factor Theorem
Find the roots of the function \(f(x) = x^3 - 9x^2 + 23x - 15\) using the factor theorem.
Finding All Possible Roots/Zeros (RRT)
Find all possible roots/zeros of the function \(f(x) = x^3 - 4x^2 + x + 6\)
Determine if Injective (One to One)
Determine whether the function is one-to-one. If it is, find a formula for its inverse.
\[
f(x)=x^{3}-1
\]
Is the function one-to-one?
Yes
No
Select the correct choice below and fill in any answer boxes within your choice.
A. The inverse function is $f^{-1}(x)=$
B. There is no inverse function.
Determine if Surjective (Onto)
Given the function \(f: \mathbb{R} \rightarrow \mathbb{R}\) defined as \(f(x) = x^2\), determine if this function is surjective (onto).
Finding the Vertex
Find the vertex of the function \(f(x) = 2x^2 - 4x + 1\).
Finding the Sum
Hallar el $9 .^{\circ}$ término de la sucesión geométrica cuya razón común es $\frac{1}{3}$ y cuyo primer término es 2 .
Finding the Difference
Let $f(x)=x^{2}$. How do the values of $f(2)$ and $f(2)+5$ differ?
Finding the Product
Find the product of the functions \(f(x) = 3x + 2\) and \(g(x) = 2x - 5\)
Finding the Quotient
Find the quotient of the functions \(f(x) = 2x^2 + 3x - 2\) and \(g(x) = x - 1\)
Finding the Domain of the Difference of the Functions
Find the domain of the difference of the functions \(f(x) = \sqrt{x}\) and \(g(x) = \frac{1}{x-2}\)
Finding the Domain of the Product of the Functions
Given the functions \(f(x) = \sqrt{x}\) and \(g(x) = \frac{1}{x}\), find the domain of the product of the functions \(h(x) = f(x)g(x)\).
Finding the Domain of the Quotient of the Functions
Find the domain of the quotient of the functions \(f(x) = x^2 - 4\) and \(g(x) = x - 2\).
Finding Roots (Zeros)
Find the roots of the function \(f(x) = 2x^2 + 3x - 2\).
Identifying Zeros and Their Multiplicities
Find the zeros and their multiplicities for the function \( f(x) = 2x^3 - 3x^2 - 11x + 6 \).
Finding the Bounds of the Zeros
Find the bounds of the zeros of the function \(f(x) = x^3 - 7x^2 + 14x - 8\)
Proving a Root is on the Interval
Prove that the function \(f(x) = x^2 - 4x + 4\) has at least one root in the interval \([1, 2]\).
Finding the Average Rate of Change
Aysha has a big backyard garden. When she measured the height of the tree, it was 14 feet tall. After one year, it was 16 feet tall. Assuming that the tree grows constantly at this rate.
Determine the function that represents the height \( (H) \) of the tree each year.
a. \( H(y)=15+y \)
b. \( H(y)=14+2 y \)
c. \( H(y)=16+y \)
d. \( H(y)=16-2 y \)
Finding the Inverse
The following functions are inverses of each other. $f(x)=5 x-9$ and $g(x)=\frac{x+5}{9}$
False
Finding Maximum Number of Real Roots
What is the maximum number of real roots for the function \(f(x) = x^5 - 4x^3 + 2x^2 - 8\)?
Function Composition
Let $h(x)=4 x+1$. Find $(h \circ h)(x)$ $(h \circ h)(x)=$ type your answer...
Rewriting as a Function
Introduction to Functions: Vocabulary
Given the function $L(S)=c$, which of the following statements are true? Check all that are correct.
$L$ is the name of the function, $c$ is the independent variable and $S$ is the dependent variable.
$\mathrm{L}$ is the name of the function, $\mathrm{S}$ is the input variable, and $\mathrm{c}$ is the output variable.
$L$ is the name of the function, $S$ is the independent variable and $c$ is the dependent variable.
$c$ is the name of the function, $S$ is the dependent variable and $L$ is the independent variable
$c$ is the name of the function, $S$ is the input variable, and $L$ is the output variable.
$\mathrm{C}$ is the name of the function, $\mathrm{L}$ is the dependent variable and $\mathrm{S}$ is the independent variable
$L$ is the name of the function, $c$ is the input varisble, and $S$ is the output variable.
$\mathrm{c}$ is the name of the function, $\mathrm{c}$ is the dependent Variable, and $\mathrm{S}$ is the Independent Variable.
Finding the Domain and Range
The graph below shows the relationship between minutes left and days of the month of your cellular phone plan. The relationship can be modeled by the equation $f(x)=-\frac{5}{2} x+60$, where $y$ is the number of minutes left and $x$ is the day of the month. Which statement is true?
There is no $x$-intercept or $y$-intercept.
The domain is all real numbers.
The range is all whole numbers greater than or equal to 0 and less than or equal to 60
The function has no maximum value.
Determining if a Function is Rational
The function in the table is quadratic:
\begin{tabular}{|l|l|}
\hline & $f(x)$ \\
\hline-1 & -7 \\
\hline 0 & 1 \\
\hline 1 & 9 \\
\hline 2 & 17 \\
\hline
\end{tabular}
True
False
Determining if a Function is Proper or Improper
Determine whether the following function is proper or improper: \(f(x) = \frac{4x^2 + 5x + 2}{2x^2 + 3x + 1}\)
Maximum/Minimum of Quadratic Functions
Find the maximum value of the quadratic function \(f(x) = -2x^2 + 4x + 3\).
Finding the Slope
What is the slope of the line represented by the function \(f(x) = 7x - 3\)?