Analyzing Graphs of Functions and Relations

The video tutorial covers analyzing graphs of functions and relations, focusing on domain and range, intercepts, zeros, symmetry, and identifying even and odd functions. It provides examples and algebraic methods to find these properties, enhancing understanding of graph behavior and function characteristics.

What is the domain of a function?

• The set of all y-values used to graph the function

• The set of all x-values used to graph the function

• The set of all points where the graph intersects the y-axis

• The set of all points where the graph intersects the x-axis

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

In the given example, what is the domain of the function F?

• [-8, -4) ∪ (-4, ∞)

• (-8, -4] ∪ (-4, ∞)

• [-8, -4] ∪ (-4, ∞)

• (-8, -4) ∪ [-4, ∞)

How do you find the y-intercept of a function algebraically?

• Set y to zero and solve for x

• Find the point where the graph crosses the y-axis

• Set x to zero and solve for y

• Find the point where the graph crosses the x-axis

What is the y-intercept of the function G in the example?

• 1.3

• 4

• 4/3

• 0

What are the zeros of a function also called?

• Asymptotes

• Extremes

• Roots

• Intercepts

Tags

CCSS.HSF-IF.C.7C

How do you test for symmetry with respect to the x-axis?

• Replace y with -y and check if the equation remains the same

• Replace x with -x and check if the equation remains the same

• Replace both x and y with their negatives and check if the equation remains the same

• Check if the graph is a mirror image across the y-axis

Tags

CCSS.HSF.BF.B.3

What does it mean if a function is symmetric with respect to the origin?

• The graph is a mirror image across the x-axis

• For every point (x, y), the point (x, -y) is also on the graph

• For every point (x, y), the point (-x, y) is also on the graph

• For every point (x, y), the point (-x, -y) is also on the graph

Tags

CCSS.HSF.BF.B.3

What is the definition of an even function?

• A function symmetric with respect to the x-axis

• A function symmetric with respect to the y-axis

• A function symmetric with respect to the origin

• A function that has no symmetry

Tags

CCSS.HSF.BF.B.3

Which of the following is true for an odd function?

• f(x) = f(-x)

• f(x) = -f(-x)

• f(-x) = -f(x)

• f(-x) = f(x)

Tags

CCSS.HSF.BF.B.3

What is the symmetry of the function G(x) = x^4 + 2?

• Symmetric about the origin

• No symmetry

• Symmetric about the y-axis

• Symmetric about the x-axis

Tags

CCSS.HSF.BF.B.3