Lesson Menu FiveMinute Check over Lesson 3 7

Lesson Menu Five-Minute Check (over Lesson 3– 7) Mathematical Practices Then/Now New Vocabulary Key Concept: Absolute Value Function Example 1: Graphing f (x) + k Example 2: Graphing f (x – h) Example 3: Graphing a • f (x) Example 4: Graphing f (bx) Example 5: Real-World Example: Absolute Value Function

Warm-up What is the function shown in the graph? What is the domain and range of the graph? The graph shows the cost of parking at a parking garage. Which interpretation of the graph is not correct?

Over Lesson 3 -7 Which function is shown in the graph? A. C. B. D.

Over Lesson 3 -7 What is the domain and range of f(x)? A. D = all real numbers; R = y > 2 B. D = all real numbers; R = y > – 2 C. D = all real numbers; R = – 2 < y < 2 D. D = all real numbers; R = all real numbers

Over Lesson 3 -7 The graph shows the cost of parking at a parking garage. Which interpretation of the graph is not correct? A. The cost to park for the first hour is $4. B. The cost to park for hours is $10. C. The cost to park after the first hour increases by $4 per hour. D. The cost to park for more than 6 hours is $16.

Ch. 3 -8 Absolute Value Functions

Mathematical Practices 7 Look for and make use of structure. Content Standards F. IF. 7 b Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions. F. BF. 3 Identify the effect on the graph of replacing f (x) by f (x) + k, k f (x), f(kx), and f (x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

You identified and graphed piecewise and step functions. • Identify and graph translations of absolute value functions. • Identify and graph reflections and dilations of absolute value functions.

• absolute value function • vertex

Graphing f (x) + k Graph g(x) = |x| + 4. State the domain and range, and describe how the graph is related to the graph of f(x) = |x|. Vertex is where? Answer: D: all real numbers; R: y ≥ 4; translation 4 units up

Graphing f(x – h) Graph g(x) = |x + 3|. State the domain and range, and describe how the graph is related to the graph of f(x) = |x|. Vertex is where? Answer: D: all real numbers; R: y ≥ 0; translation 3 units left

Graphing a • f (x) Vertex is where? Answer: D: all real numbers; R: y ≤ 0; reflection across the x-axis and vertical compression by a factor of 1 3

Graphing f(bx) Vertex is where? Answer: D: all real numbers; R: y ≥ 0; horizontal stretch by a factor of 3 and reflection across the y-axis (although the reflection is not apparent)

Absolute Value Function SPORTS The function f(x) = 2|x – 25| models a swimmer’s distance in meters from the far end of the pool after x seconds. Graph this function. How many meters is the swimmer from the far end of the pool when timing begins? Answer: 50 m