Understanding Absolute Value Functions

The video tutorial explains how to graph an absolute value function using its vertex and intercepts. It begins by identifying the standard form of the function and determining the vertex and direction based on the value of 'a'. The tutorial then demonstrates how to find the horizontal (x-intercepts) and vertical (y-intercept) intercepts by setting the function equal to zero and evaluating f(0), respectively. Finally, it shows how to plot these points on a graph to visualize the function.

What is the standard form of an absolute value function?

• f(x) = a(x - h)^2 + k

• f(x) = a|x - h| + k

• f(x) = a(x + h) + k

• f(x) = ax + b

If the parameter 'a' is positive in an absolute value function, what is the orientation of the 'V' shape?

• The 'V' is vertical

• The 'V' opens upwards

• The 'V' opens downwards

• The 'V' is horizontal

How do you determine the value of 'h' in the function f(x) = 2|x + 3| - 4?

• h is 4

• h is -4

• h is -3

• h is 3

What is the vertex of the function f(x) = 2|x + 3| - 4?

• (-3, 4)

• (3, 4)

• (3, -4)

• (-3, -4)

What is the first step in finding the horizontal intercepts of an absolute value function?

• Set y equal to zero

• Set the derivative equal to zero

• Set f(x) equal to zero

• Set x equal to zero

What are the horizontal intercepts of the function f(x) = 2|x + 3| - 4?

• (0, 5) and (0, 1)

• (-3, 0) and (3, 0)

• (5, 0) and (1, 0)

• (-5, 0) and (-1, 0)

How do you find the vertical intercept of an absolute value function?

• Set f(x) equal to zero

• Set the derivative equal to zero

• Set x equal to zero

• Set y equal to zero

What is the vertical intercept of the function f(x) = 2|x + 3| - 4?

• (0, -2)

• (-2, 0)

• (2, 0)

• (0, 2)

Which points are used to graph the absolute value function?

• Only the vertex

• Only the intercepts

• The vertex and intercepts

• None of the above

What is the significance of the vertex in graphing an absolute value function?

• It is where the graph crosses the y-axis

• It is where the graph crosses the x-axis

• It is the highest or lowest point

• It determines the slope