Translating Function Equations to Graphs

This video lesson by Kirk Weiler covers Unit 3, Lesson 3 of Common Core Algebra 1, focusing on graphs of functions. It begins with an introduction to resources available for the lesson, including worksheets and QR codes. The lesson then delves into understanding graphs of functions, emphasizing function notation and the relationship between inputs and outputs. It covers graphing linear functions using tables, introduces quadratic functions and their parabolic graphs, and explains piecewise functions with examples. The lesson concludes with a summary of key points about functions and graphs.

What is the primary focus of this lesson?

• Solving equations

• Graphs of functions

• Arithmetic operations

• Geometry

In function notation, what does f(4) represent?

• The input value

• The output value when x is 4

• The y-intercept

• The slope of the function

What is the y-coordinate when the x-coordinate is 4 in the given graph?

• 2

• 3

• 1

• 4

For what x-values does f(x) equal -2?

• x = -1 and x = 1

• x = 1 and x = 3

• x = 0 and x = 2

• x = -2 and x = 2

What is the minimum value of the function in Exercise 1?

• -3

• 3

• 6

• 0

What is the rule for the function G(x) in Exercise 2?

• G(x) = x + 3

• G(x) = x - 3

• G(x) = 3x + 2

• G(x) = 2x + 3

What is the output when the input is -2 for the function G(x) = 2x + 3?

• -1

• 1

• 3

• -3

What is the highest power of x in a quadratic function?

• 4

• 1

• 3

• 2

What shape does the graph of a quadratic function form?

• Circle

• Ellipse

• Parabola

• Line

In a piecewise defined function, what determines which rule to use?

• The intercept

• The x-value

• The y-value

• The slope