Graphing Piecewise Functions: Key Concepts and Techniques

The video tutorial explains how to graph piecewise functions by combining two separate functions, f(x) = x + 2 and f(x) = 3x, using the slope-intercept method. It discusses the importance of domain constraints to ensure the combined graph remains a function. The tutorial also covers how to finalize the piecewise graph and analyze its domain and range, ensuring all x-values are covered. The video concludes with a discussion on the range of the piecewise function.

What is the main goal when working with piecewise functions?

• To solve for x

• To graph both functions and combine them

• To determine the range

• To find the intersection points

Tags

CCSS.HSF-IF.C.7B

What is the y-intercept of the function f(x) = x + 2?

• 0

• 1

• 2

• 3

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

What is the slope of the function f(x) = x + 2?

• 3

• 2

• 1

• 0

Tags

CCSS.8.EE.B.5

What is the y-intercept of the function f(x) = 3x?

• 0

• 1

• 2

• 3

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

What is the slope of the function f(x) = 3x?

• 0

• 1

• 2

• 3

Tags

CCSS.8.EE.B.5

Why can't the two graphs be combined without constraints?

• They have different slopes

• They have different y-intercepts

• They would not form a function

• They intersect at multiple points

Tags

CCSS.HSF-IF.C.7B

What is the domain of the function f(x) = x + 2 in the piecewise function?

• x > -2

• x ≥ -2

• x < -2

• x ≤ -2

Tags

CCSS.HSF-IF.C.7B

What is the domain of the function f(x) = 3x in the piecewise function?

• x ≤ -2

• x < -2

• x > -2

• x ≥ -2

Tags

CCSS.HSF-IF.C.7B

What is the overall domain of the piecewise function?

• Negative infinity to -2

• 2 to infinity

• Negative infinity to infinity

• 0 to infinity

Tags

CCSS.HSF-IF.C.7B

What is the range of the piecewise function?

• Negative numbers only

• 0 to infinity

• All real numbers

• Positive numbers only

Tags

CCSS.HSF-IF.C.7B