Absolute Value Functions and Translations / Instruction / summary / assignment

What are the coordinates of the vertex of the graph? The vertex is ______

(-2, 1)

Graph f(x) = l x - 2 l -4

Step 1: to the right / down Step 2: (2, -4) Step 3: -3 Step 4: (3, -3)

Graph f(x) = lxl + 3

Step 1: up Step 2: plot (0, 3) Step 3: 4 / 4

The graph of f(x) = |x - h| + k contains the points (-6, -2) and (0, -2). The graph has a vertex at (h, -5). Describe how to find the value of h. Then, explain how this value translates the graph of the parent function.

Sample Response: The absolute value function is symmetric with its vertex on the line of symmetry. Because the points (-6, -2) and (0, -2) have the same output, the points are the same distance from the line of symmetry. Midway between -6 and 0 is the value of -3. Therefore, the vertex must have an x-coordinate of -3, which is the value of h. This would translate the graph of the parent function 3 units to the left.

What are the domain and range of f(x) = |x - 3 | + 6? Domain: {x | x is all real numbers}Range: {y | y ≥ 6} Domain: {x | x ≥ 3}Range: {y | y ≥ 6} Domain: {x | x is all real numbers}Range: {y | y ≥ - 6} Domain: {x | x ≥ 3}Range: {y | y ≥ - 6}

Domain: {x | x is all real numbers}Range: {y | y ≥ 6}

Which phrases describe the graph of f(x) = |x| ? Check all that apply. V-shaped U-shaped opens up opens down symmetric with respect to the x-axis symmetric with respect to the y-axis

V-shaped opens up symmetric with respect to the y-axis

Describes f(x) = lxl : graph opens up range: {y l y greater than or equal to 0} is increasing over (0, infinity) vertex at (0, 0) Does not Describe f (x) = lxl : domain: {x l x greater than or equal to 0} symmetric with respect to x-axis

answer on front

The graph of f(x) = |x| has been translated left 2 units and up 1 unit. If no other transformations of the function have occurred, which point lies on the new graph? (-4, 2) (-3, 1) ( -2, 5) ( -1, 2)

( -1, 2)

The vertex of the graph of f(x) = |x - 3| + 6 is located at

(3, 6)

Graph: y = lx -4 l + 2 On which interval is the function increasing? (-∞, -4) (-∞, 4) (-4, ∞) (4, ∞)

(4, 2) / (4, ∞)

Which graph represents the function h(x) = |x - 3|?

C

Which function is represented by the graph? f(x) = |x - 1| + 3 f(x) = |x + 1| - 3 f(x) = |x - 1| - 3 f(x) = |x + 1| + 3

f(x) = |x + 1| - 3

Which functions could be represented by the graph? Check all that apply. f(x) = | x + 0.14| f(x) = |x| + 1.3 f(x) = |x - 7| f(x) = |x + 12| f(x) = |x| - 17 f(x) = |x - 23|

f(x) = |x - 7| f(x) = |x - 23|

Which function is represented by the graph? g(x) = |x + 2.5| g(x) = |x| + 2.5 g(x) = |x - 2.5| g(x) = |x| - 2.5

g(x) = |x| + 2.5

The graph shows f(x) = |x - h| + k. What is the value of h? h = 2.5 h = -1.5 h = 1.5 h = -2.5

h = 2.5

Which function is represented by the graph? The parent absolute value function is translated _______ 3 units and _______ 1 unit. The function that is graphed is f(x) = ________

left / up / l x + 3 l +1

The graph of the parent function f(x) = |x| is dashed and the graph of the transformed function g(x) = |x - h| is solid. Use the slider to change the value of h. How does changing the value of h affect the vertex? Positive values of h shift the graph _______ Negative values of h shift the graph_______

right / left

The graph of the parent function f(x) = |x| is dashed and the graph of the transformed function g(x) = |x| + k is solid. Use the slider to change the value of k. How does changing the value of k affect the graph? Positive values of k shift the graph______ Negative values of k shift the graph______

up / down

Complete the statements for the graph of f(x) = |x|. The domain of the function is The range of the function is The graph is ________ over the interval (0, ∞). The graph is _______ over the interval (-∞, 0).

{x lx is all real numbers} / {y l y is greater than or equal to zero} / increasing / decreasing

The function g(x) = |x - 6| - 8 is graphed. What is the range? {y | y > -8} {y | y ≥ -8} {y | y < -8} {y | y is all real numbers}

{y | y ≥ -8}