Understanding Linear Functions and Their Properties

The video tutorial explains the concept of functions, focusing on f(x) and g(x) functions. It demonstrates how to calculate the output of these functions for given inputs and solve equations where the function equals a specific value. The tutorial uses examples to illustrate these concepts, such as finding f(2) and g(-3), and solving f(x)=15 and g(x)=22.

What is the main concept of a function as introduced in the video?

• A function is a type of number.

• A function is a type of graph.

• A function is a relationship between inputs and outputs.

• A function is a method to solve equations.

If f(x) = 2x + 3, what is f(2)?

• 7

• 8

• 6

• 5

What is the result of f(-3) if f(x) = 2x + 3?

• 6

• 3

• 0

• -3

How do you solve for x when f(x) = 15 in the equation f(x) = 2x + 3?

• Add 3 to 15 and divide by 2.

• Divide 15 by 2 and add 3.

• Subtract 3 from 15 and divide by 2.

• Multiply 15 by 2 and subtract 3.

What is the new function introduced in the video?

• g(x) = 5x - 3

• k(x) = 4x - 1

• h(x) = 3x + 2

• f(x) = 2x + 3

If g(x) = 5x - 3, what is g(2)?

• 9

• 11

• 7

• 5

What is the result of g(-3) if g(x) = 5x - 3?

• -9

• -12

• -15

• -18

How do you solve for x when g(x) = 22 in the equation g(x) = 5x - 3?

• Divide 22 by 5 and subtract 3.

• Multiply 22 by 5 and add 3.

• Subtract 3 from 22 and divide by 5.

• Add 3 to 22 and divide by 5.

What is the output of the function g(x) = 5x - 3 when x = 0?

• 5

• 0

• -3

• 3

Which of the following is true about the functions f(x) and g(x)?

• f(x) is a linear function, while g(x) is not.

• Both functions have the same output for any input.

• Both functions are linear but have different coefficients.

• g(x) is a quadratic function.