Exploring Linear Functions

The video tutorial covers the basics of function notation, focusing on linear, quadratic, and exponential functions. It emphasizes the importance of understanding the slope and y-intercept in linear functions, providing examples and practice problems. The tutorial also guides students on how to solve for the y-intercept using given points and prepares them for final exam questions.

What are the general equations for linear, exponential, and quadratic functions?

• f(x) = mx + b, f(x) = ab^x, f(x) = ax^2 + bx + c

• f(x) = ax + b, f(x) = ab^x, f(x) = ax^2 + bx

• f(x) = ax + b, f(x) = ab^x, f(x) = ax^2 + bx + c

• f(x) = mx + b, f(x) = ab^x, f(x) = ax^2 + b

What does f(x) represent in function notation?

• The input value

• The output value depending on x

• The slope of the function

• The y-intercept of the function

In the slope formula, what does the 'rise' represent?

• The slope

• The change in x-coordinates

• The change in y-coordinates

• The y-intercept

How do you find the y-intercept from a table of values?

• Look for the value of y when x is zero

• Look for the value of x when y is zero

• Calculate the slope first

• Use the slope formula

What is the slope of the line passing through the points (0, 80) and (10, 95)?

• 15/10

• 3/2

• 5

• 7/2

What is the equation of the linear function passing through the points (0, 80) and (10, 95)?

• f(x) = 3/2x + 80

• f(x) = 7/2x + 9

• f(x) = 3x + 80

• f(x) = 2x + 95

How do you handle a negative value in the slope formula?

• Subtract it from the other value

• Add it to the other value

• Ignore it

• Treat it as a positive value

What is the slope of the line passing through the points (-4, -5) and (-2, 2)?

• 2

• 5

• 3/2

• 7/2

What is the y-intercept of the line passing through the points (-4, -5) and (-2, 2)?

• 5

• 9

• 7

• 2

Which of the following is true about the functions f(x) and g(x) given in the practice problem?

• They have the same y-intercept

• They are never equal

• They have the same slope

• They are always equal