Warm Up – August 21, 2017 Find the x- and y-intercepts. X – 3y = 9

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Presentation transcript:

Warm Up – August 21, 2017 Find the x- and y-intercepts. X – 3y = 9 Y = 7x + 5 Write the equation of the line in slope-intercept form and identify the slope. 3. 2x – y = 9 4. 4x = 2 + y Write and equation of each line in standard form with integer coefficients. 5. The line through (2, 3) and (4, 5) 6. The line through (1, 2) with slope 4/5 7. 2y = -4x – 12 For each function, determine whether y caries directly with x. If so, identify the constant of variation. 8. 2y = 3x 9. 4y – x = 16

2.6 Families of Functions Learning Target: I can transform linear functions. Key terms: parent function, transformation, translating, reflection, vertical stretch, vertical compression

Key Terms: Parent function – the simplest form in a set of functions that form a family. Transformation – a change to the parent function y = x Translation – when the function is shifted Reflection – when the function is flipped over the x- or y-axis Vertical stretch – multiplies all y-values of a function by the same factor greater than 1. Vertical compression – reduces all y-values of a function by the same factor between 0 and 1.

“I do” Vertical Translation How are the functions y = x and y = x – 2 related? How are their graphs related?

“You do” How are the functions y = 2x and y = 2x – 3 related? How are their graphs related?

“I do” Reflecting a Function Algebraically Let g(x) be the reflection of f(x) = 3x + 3 in the y-axis. What is a function rule?

“You do” Let g(x) be the reflection of f(x) = 2x – 3 in the y-axis. What is a function rule?

“I do” Stretching and Compressing a Function The table represents the function f(x). What are corresponding values of g(x) and possible graphs for the transformation g(x) = 3f(x)? x f(x) 3f(x) g(x) -5 2 -2 -3 3 1 5

“You do” For the function f(x) shown in the “I do”, what are the corresponding table and graph for the transformation h(x) = 1/3f(x)? x f(x) 1/3f(x) g(x) -5 2 -2 -3 3 1 5

“I do” Combining Transformations The graph of g(x) is the graph of f(x) = 4x compressed vertically by the factor ½ and then reflected in the y-axis. What is a function rule for g(x)? What transformations change the graph of f(x) to the graph of g(x)? f(x) = 2x2 g(x) = 6x2 – 1

“You do” The graph of g(x) is the graph of f(x) = x stretched vertically by a factor of 2 and then translated down 3 units. What is the function rule for g(x)? What transformations change the graph of f(x) = x to the graph of g(x) = 1/2x + 2?

Homework pg. 104 # 10, 14, 16, 19, 20, 24, 26, 30, 32