Functions and Modeling Online Quiz Questions

Which relation is a function?

True or false: The expression $f(x)$ means the function name $f$ multiplied by the input $x$.

Select all statements that correctly describe domain restrictions for the given formulas.

A table gives $f(0)=2$, $f(1)=5$, $f(2)=8$, and $f(3)=11$. Which linear rule matches the table?

True or false: A graph represents a function if every vertical line intersects it at most once.

Let $f(x)=\sqrt{x}$ and $g(x)=x-3$. What is the domain of $(f\circ g)(x)$? Enter your answer in interval notation.

For the periodic model $y=A\sin(B(x-h))+D$, select all correct statements.

Explain what an inverse function does and state the key condition a function must satisfy in order to have an inverse function. Include at least one consequence for its domain, range, or graph.

Let $f(x)=2x+1$ and $g(x)=x^2$. What is $(f\circ g)(x)$?

Which relation represents a function?

True or false: If $y=f(x)$, then $y=f(-x)$ is the reflection of the graph across the $y$-axis.

The parent function is $f(x)=x^2$. What is the vertex of $g(x)=(x-4)^2+2$?

A cost model is $C(n)=12n+150$, where $n$ is the number of units. What is $C(20)$?

What graph test determines whether a function is one-to-one?

If $f(x)=3x-5$, which formula gives $f^{-1}(x)$?

What is the period of the model $y=3\sin(4(x-1))+2$, when the angle is measured in radians?

For $f(x)=(x-2)^2+3$, what is the minimum output value? Enter the value as a number.

A function f has range [-3, 4]. Define g(x)=2f(x)-5. What is the range of g?