Finding the Range of a Function, Algebraically
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- If you recall first learning about range many years ago, you may have thought about it as subtracting the lowest value from the highest value in a dataset. We will now be taking…
By Vatsal Ojha, Alex Federspiel, Caroline K, Anusha Rahman
- While graphing functions can help us find the range of a function, sometimes it's easier to find the range algebraically, using a different set of techniques and ideas. Recall t…
By Joshua Siktar, Victor Wang, Gabi Slizewska, Anusha Rahman
- (Video) Finding the Range of a Function Algebraically by Anusha Rahman In this lesson, you will how to find the range of a function algebraically. Summary The range of a functio…
By Anusha Rahman
- Finding Function Range: Algebraically The find the range of a function algebraically, you first need to understand the values the function can output. For example, if you have a…
By Anusha Rahman
Problems 23
- Which of the following are in the range of the function f(x)=x2f(x) = x^2f(x)=x2?
- What are the domain and range of the function graphed above?
- Which of the following values are in the range of the function f(x)=πxf(x) = \frac{\pi}{x}f(x)=xπ?
- Let A⊆RA \subseteq \mathbb{R}A⊆R. Given AAA, is it always possible to construct a (not necessarily continuous) function f:R→Rf: \mathbb{R} \to \mathbb{R}f:R→R, where f(x)f(x)f(x…
- What value is not in the range of y=x−1y=x^{-1}y=x−1?
- What values are in the range of y={xx+3−3<x<−1−12x≥−1y=\begin{cases}\frac{x}{x+3}&-3<x<-1\\-\frac12&x\geq-1\end{cases}y={x+3x−21−3<x<−1x≥−1
- What values are in the range of y=x2−1xy=x^2-\frac{1}{\sqrt{x}}y=x2−x1?
- True or False\text{True or False}True or False === There are no functions that have a domain but no range.
- Determine which of the following are in the range of the function f(x)=1x−5f(x)= \dfrac{1}{x-5}f(x)=x−51.
- Which of the following are in the range of the function f(x)=1x−1+xf(x)=\dfrac{1}{x-1}+xf(x)=x−11+x?
- What is the range of the function x2+1+1\sqrt{x^2 + 1} + 1x2+1+1, given that the domain is all real numbers?
- Solve cos3(α)−sin3(α)=0\cos^3(\alpha) - \sin^3(\alpha) = 0cos3(α)−sin3(α)=0 on the interval [0,π].[0, \pi].[0,π].
- Find the range of f(x)=xx.f(x) = x\sqrt{x}.f(x)=xx.
- Which of the following numbers are in the range of f(x)=1xf(x) = \frac{1}{\sqrt{x}}f(x)=x1?
- What is the range of f(x)=x2+1f(x) = \sqrt{x^2+1}f(x)=x2+1?
- Which of the following is in the range of f(x)=x+x+1f(x) = \sqrt{\sqrt{x}+\sqrt{x+1}}f(x)=x+x+1?
- Find the range of f(x)=∣x∣−1∣x∣f(x) = \frac{|x|-1}{|x|}f(x)=∣x∣∣x∣−1.
- Which of the following is in the range of f(x)=x+1xf(x) = x+\frac{1}{x}f(x)=x+x1?
- Which of the following are in the range of f(x)=4x2+4xf(x) = \frac{4}{x^2} + \frac{4}{x}f(x)=x24+x4?
- What is the range of the function f(x)=secxf(x)=\sec{x}f(x)=secx? Hint: secx=1cosx\sec{x}=\frac{1}{\cos{x}}secx=cosx1.
- Find the range of f(x)=2xf(x) = 2^{\sqrt{x}}f(x)=2x.
- Select all values below that are in the range of f(x)=2∣x∣−2f(x) = \sqrt{2}^{|x|-2}f(x)=2∣x∣−2.
- While on top of a building, Amelia throws a bouncy ball upward. The ball lands back on the roof of the same building. The building she's is standing on is 303030 feet off the gr…