Graphing Common Functions: Videos & Practice Problems

If $f\left(x\right)=-3$, what is the range of $f$?

A graph shows the horizontal line $y=4$. Which statement correctly describes its domain and range?

Evaluate the identity function $f\left(x\right)=x$ at $x=\pi$.

Which description correctly states the range of $f\left(x\right)=x^2$?

Solve for $x$ given $f\left(x\right)=x^2$ and $f\left(x\right)=49$.

Compute $f\left(16\right)$ for $f\left(x\right)=\sqrt{x}$ and explain why this input is allowed.

Describe the domain and range of $f\left(x\right)=x^3$.

For $f\left(x\right)=x^3$, what is $f(-2)$?

Why is $x=-1$ not in the domain of $f\left(x\right)=\sqrt{x}$ when considering real-valued functions?

Explain why f(x) = ∛x has domain all real numbers while f(x) = √x does not. Which mathematical property accounts for this difference?

Compute $x$ given $\sqrt[3]{x}=-4$.

You are shown a graph of a function that looks like a right-opening curve beginning at the point (0,0) and increasing to the right with no left extension. Which common function does this describe and what are its domain and range?

Consider the graph of $y=x^2$. Which of these points is not on the graph?

Which of the following lists the functions that never produce negative outputs for any input in their natural domain?

A student claims the function f(x) = x³ and g(x) = ∛x are identical because both have domain and range all real numbers. Evaluate the correctness of this claim and choose the best assessment.

Which pair of points is consistent with the square root function $y=\sqrt{x}$?

Which of these best describes how to check whether ordered pairs belong to $f\left(x\right)=x$?

A graph passes through the points: $(-2,-8)$, $(0,0)$, and $(2,8)$. A student argues that the function must be $f\left(x\right)=x^3$. Which of the following statements is considered the best justification for accepting the student's conclusion?

Which explanation correctly justifies why $f\left(x\right)=x^2$ never outputs a negative number?

A researcher measures a quantity $y$ that follows $y=\sqrt{t}$, where $t$ is time in seconds. If $y=9$, how many seconds have elapsed?

Which of the following is true for the identity function $f\left(x\right)=x$?

Which pair of functions are both continuous for all real numbers and one-to-one (invertible) over all real numbers?

If a function satisfies $f\left(7\right)=f\left(0\right)=5$ and is known to be constant, what is $f\left(x\right)$ for any real $x$?

Which of the following pairs of functions are odd functions?

A data table shows x: -2, -1, 0, 1, 2 and y: -8, -1, 0, 1, 8. A student must choose which common function best models this data. Which function should they choose and why?

For which of these functions is $f(-3)>0$?

Which common function best matches this description: continuous on all real numbers, odd symmetry about the origin, and increases from -∞ to ∞?

Which interval notation correctly gives the domain of $f\left(x\right)=\sqrt{x}$ for real-valued outputs?

Given $f\left(x\right)=x$ and $g\left(x\right)=x^2$, which of these points lies on both graphs?

A graph of an unknown common function shows the point $(9,3)$. Which of these functions could this point belong to, and which is the most specific fit?