What is a Function? - Definition & Examples
Read this topicExplanations 5
- We can think of functions as a machine. We can plug in a value, and our machine will do something to it, and it will output a result. For example, f(x)=2x+3f(x)=2x+3f(x)=2x+3 is…
By Evan Tong, Alex Federspiel, Ruiran Xun, Amy Feraco, Sarah Walker
- Functions - What are Those?! In math, think of a function like a little machine. We give it an input, like putting a penny into a gumball machine. The job of the function is to …
By Hannah Bonville, Zora Gilbert, Alex Federspiel, Anusha Rahman
- (Video) What are Functions? by Math Antics In this video, mathantics explains what a function is. Summary\large{\text{Summary}}Summary Function: Something that relates or connec…
By Alex Federspiel, Zora Gilbert, Amy Feraco
- (Video) Introduction to Functions by mathman1024 In this video, mathman1024 explains the basics of functions. Summary\large{\text{Summary}}Summary Here's an example of a relatio…
By Alex Federspiel, Zora Gilbert, Amy Feraco, Sarah Walker, Anusha Rahman
- (Video) Functions and Relations by Eddie Woo Here's a video by Eddie Woo where he briefly goes over the fundamentals of functions. Summary\large{\text{Summary}}Summary What are …
By Alex Federspiel, Victor Wang, Amy Feraco, Sarah Walker, Anusha Rahman
Problems 30
- Evaluate the function f(x)=2x+1f(x)=2x+1f(x)=2x+1 at x=−7x=-7x=−7.
- Evaluate the function f(x)=x2−8f(x)=x^2-8f(x)=x2−8 at x=6x=6x=6.
- A pool is being filled with water from a hose that gives out a certain number of liters per minute. If we write a function of the volume of water in the pool, what are the indep…
- In the function rule h(t)=3t2+2t+1h(t)=3t^2+2t+1h(t)=3t2+2t+1, what are the independent and dependent variables? Check all that apply.
- True or False\text{True or False}True or False === A function can have more than one output for a single input as long as all the outputs are real numbers.
- Is y=x+42−5569y=\frac{x+42-55}{69}y=69x+42−55 a function of xxx? If so, identify the dependent variable in the function.
- Simon is interested in comparing temperatures in China (in Celsius) and temperatures in the US (in Fahrenheit). He finds out that the temperature in Fahrenheit is 323232 degrees…
- Fill in the blank of the statement concerning this function: "The value of yyy depends on what is 0000‾\underline{\phantom{0000}}0000 xxx."
- If you see the equations "f(x)=x2f(x) = x^2f(x)=x2" and "y=f(x)y = f(x)y=f(x)" written, what can you conclude? Select all that apply.
- What does the equation f(x)=x2f(x) = x^2f(x)=x2 say about the function fff? Select all that apply.
- How many functions f(x)f(x)f(x) are there, such that for any input value xxx, the output value y=f(x)y = f(x)y=f(x) satisfies the equation x+y=2x+y=2x+y=2?
- Suppose fff is a function given by the function rule f(x)=1f(x) = 1f(x)=1. What does the verbal expression "f of x" refer to?
- Let the amount of twitching a person does, ttt, after drinking cups of coffee, ccc, be given by t=f(c)t=f(c)t=f(c). What is the independent variable in this function?
- Let the amount of twitching a person does, ttt, after drinking cups of coffee, ccc, be given by t=f(c)t=f(c)t=f(c). What is the dependent variable in this function?
- What is the most reasonable interpretation of the shorthand 3↦933\mapsto 933↦93?
- Find a function ggg with the following verbal description: Start with an input nnn. First double the input. Then add 101010 to get the final output.
- Find a function AAA with the following verbal description: First add 101010 to the input sss. Then square to get the final output.
- Which function below could have the following verbal representation? Given an input, first add 101010. Then double the result to get the final output.
- Which function below could have the following verbal description? First halve the side length sss. Then square the result to get AAA, the area of the reduced picture.
- Which function below could represent the "squaring" button on a calculator?
- Which function below could represent the "reciprocal" button on a calculator?
- How can Leia achieve her goal using only these two kinds of parts? Select all possibilities.
- Using the table above, what does f(8)f(8)f(8) equal?
- Is this graph a function?
- Is the graph above a function?
- Is the graph above a function?
- Could the table above represent a function?
- Could the table above represent a function?
- If you have the function f(h)=2h−7+3kf(h)=2h-7+3kf(h)=2h−7+3k find the output when the input is 2.
- Anna is selling lunch boxes. Each box is sold at 666 dollars. It costs about 333 dollars to make the food in each box and the box itself is about 303030 cents. Let yyy denote An…