Graphing Linear Functions with Domain Restrictions

This video tutorial covers graphing linear functions on restricted domains and ranges. It begins with an introduction to the concepts of domain and range, followed by several examples demonstrating how to graph functions with specific domain restrictions, including point-slope form and integer domains. The tutorial also explores graphing with a restricted range and finding the maximum value of a function's range. The video concludes with a summary and encourages viewers to practice the concepts learned.

What is the primary focus of this video tutorial?

• Graphing quadratic functions

• Graphing linear functions on restricted domains

• Solving linear equations

• Finding the roots of polynomials

In the first example, what is the slope of the function y = 3/2x - 6?

• 2/3

• 3/2

• 2

• 1/2

How is the point at the y-intercept indicated when x > 0?

• With a star

• With an open circle

• With a filled circle

• With a dashed line

In the second example, what is the slope of the function y - 4 = -2(x + 1)?

• 1

• -2

• 2

• -1

What is the range of the function y - 4 = -2(x + 1) with domain -2 ≤ x ≤ 4?

• -6 ≤ y ≤ 6

• -4 ≤ y ≤ 4

• -2 ≤ y ≤ 2

• -8 ≤ y ≤ 8

In the third example, what is the y-intercept of the function y = 3x + 2?

• (0, 2)

• (0, 3)

• (3, 0)

• (2, 0)

Why should the points not be connected with a line in the third example?

• Because the domain is restricted to integers

• Because the slope is negative

• Because the y-intercept is not included

• Because the function is not linear

In the fourth example, what is the x-value when y = -3 for the function y = -x + 5?

• 8

• 4

• -8

• -4

What is the maximum value of the range for the function f(x) = -2x + 7 with domain -1 ≤ x ≤ 6?

• 7

• 9

• 6

• 5

If the domain of f(x) = -2x + 7 is changed to all real numbers, what would be the range?

• -7 to 7

• -∞ to ∞

• -∞ to 0

• 0 to 7