Understanding Function Rules

This video tutorial explains how to describe and write function rules from given descriptions. It covers examples of different function rules, such as h(x) = x - 5 and k(x) = 5 - x, and how to describe them in words. The tutorial also demonstrates how to convert written descriptions into symbolic function rules, using examples like f(x) = x/5 and g(x) = x + 7. Additionally, it addresses more complex operations, such as p(n) = 2(n + 1) and q(w) = 2w + 1, highlighting the importance of operation order. The video concludes with a summary of the key points discussed.

What does the function h(x) = x - 5 do to its input?

• Divides the input by 5

• Multiplies the input by 5

• Subtracts 5 from the input

• Adds 5 to the input

How is the function k(x) = 5 - x different from h(x) = x - 5?

• It adds 5 to the input

• It subtracts the input from 5

• It multiplies the input by 5

• It divides the input by 5

What operation does the function r(a) = |a| perform?

• Squares the input

• Negates the input

• Takes the absolute value of the input

• Adds 5 to the input

What is the result of the function s(t) = -t?

• The input is squared

• The input is negated

• The input is doubled

• The input is halved

How is the function f(x) = x/5 commonly written?

• As a difference x - 5

• As a product 5x

• As a sum x + 5

• As a fraction x/5

What does the function g(x) = x + 7 do to its input?

• Multiplies the input by 7

• Subtracts 7 from the input

• Adds 7 to the input

• Divides the input by 7

What is the symbolic representation of the function c(t) that squares its input?

• c(t) = t^2

• c(t) = 2t

• c(t) = t - 2

• c(t) = t + 2

What is the first step in the function p(n) = 2(n + 1)?

• Double the input

• Square the input

• Add 1 to the input

• Subtract 1 from the input

In the function q(w) = 2w + 1, what is done first?

• Double the input

• Square the input

• Add 1 to the input

• Subtract 1 from the input

Why are the function rules p(n) = 2(n + 1) and q(w) = 2w + 1 not equivalent?

• They have different input variables

• They perform operations in a different order

• They both add 1 to the input

• They both double the input