Describe the Transformation
f(x) = x2 + 8
What is translation up 8.
The quadratic function translated down 3
What is g(x) = x2 - 3
f(x) = x2 - 5
D:(-∞, ∞) R: [-5, ∞)
x2 + 8x + 12 = 0
What is x = -2, -6
Students who score within 20 points of 80 will pass a test. Write this as a distance from 80 using absolute value notation.
Let s = test score
| s – 80| ≤ 20
f(x) = lx - 4l
What is translates to the right 4
The absolute value function translated to the left 7
What is f(x) = lx + 7l
h(x) = √(x + 2)
D: [-2, ∞) R: [0, ∞)
h2 - 4h - 60 = 0
What is h = -6, 10
Solve the inequality
2|v – 7| – 4 ≥ 42
v ≤ –16 OR v ≥ 30
f(x) = 1/2x3 - 5
What is vertical compression by factor of 1/2 and down 5.
The cubic function reflected across the x-axis and translated down 5
What is h(x) = -x3 - 5
g(x) = |x - 1|
D: (-∞, ∞) R: [0, ∞)
2x2 + 18x -20 = 0
What is x = -10, 1
f(x)= –3|x – 2| –1
No real x-intercepts
Y-intercept at (0, –7)
f(x) = –√(x + 9) - 2
What is translates left 9, reflection across x-axis, and down 2.
The square root function translated right 8 and down 10
What is f(x) = √(x - 8) - 10
f(x) = (x + 2)3 - 6
D: (-∞, ∞) R: (-∞, ∞)
4x2 + 56x + 160 = 0
What is x = -10, -4
Describe the transformations to the function and graph the function
f(x) = 2|x + 3| + 1
Transformations: left 3 units, vertical stretch by factor of 2, up 1 unit
f(x) = –3lx - 5l - 6
What is translates right 5, reflection across x-axis, vertical stretch by factor of 3, and down 6
The absolute value function reflected over the x axis, vertical stretch by factor of 2, left 3, and up 4
What is g(x) = -2lx + 3l + 4
g(x) = -(x - 5)2 + 7
D: (-∞, ∞) R: [7, -∞)
Find the zeros AND vertex of x2 - 2x + 35 = 0
What is x = -5, 7 and vertex (1, 34)
Describe the transformations to the function and graph the function
g(x) = |3x + 9| + 2
Rewrite function as:
g(x) = |3(x+3)|+2
Transformations: Left 3 units, horizontal compression by factor of 1/3, up 2 units