Unit 3 Review

The function f is defined as f(x) = -x + 5 . The function is translated 8 units down. What is the equation for the transformed function, g ? Choose the correct option.

• $ g(x) = -x + 13 $

• $ g(x) = -x - 3 $

• $ g(x) = -x + 5 $

• $ g(x) = -x - 8 $

If a function $ y = f(x) $ has a y-intercept at (0, 10), then the function $ y = f(x) - 6 $ has a y-intercept at (0, n). What is the value of n?

• 4

• 6

• 10

• 16

The table shows values for a quadratic function, $ g $. What is the equation for the axis of symmetry?

• x = -2

• x = 0

• x = 1

• x = 4

An absolute value function, f , is graphed such that y = f(x) . Which of the following is an equation for the function?

• y = |x|

• y = x^2

• y = x + 2

• y = 2x

An absolute value function, f, is graphed such that y = f(x). Find all values of $ x $ that make $ f(x) = 5 true.

• x = 5

• x = -5

• x = 0

• x = 10

The equation of a circle is \((x + 7)^2 + (y - 13)^2 = 50\). Identify the center and radius of the circle. (Any answers in simplest radical form, when necessary)

• Center: (-7, 13), Radius: \(\sqrt{50}\)

• Center: (7, -13), Radius: \(5\)

• Center: (-7, -13), Radius: \(\sqrt{25}\)

• Center: (7, 13), Radius: \(10\)

The function $ f $ is obtained from translating the parent function $ y = \sqrt{x} $ right 6 units and reflecting over the $ x $-axis. Which of the following is the equation for the function $ f $?

• $ f(x) = -\sqrt{x - 6} $

• $ f(x) = \sqrt{x + 6} $

• $ f(x) = -\sqrt{x + 6} $

• $ f(x) = \sqrt{x - 6} $

Let f(x) = sqrt{x+3} - 2. Determine the domain and range of f(x) in interval notation.

• Domain: [-3, ∞), Range: [-2, ∞)

• Domain: (-∞, 3], Range: (-∞, 2]

• Domain: [3, ∞), Range: [2, ∞)

• Domain: (-3, ∞), Range: (-2, ∞)

The function $ f $ is obtained from translating the parent function $ y = \sqrt{x} $ down 3 units and reflecting over the $ y $-axis. What is the equation for the function $ f $? Choose the correct option.

• $ f(x) = -\sqrt{x} - 3 $

• $ f(x) = \sqrt{-x} - 3 $

• $ f(x) = -\sqrt{-x} - 3 $

• $ f(x) = \sqrt{x} + 3 $

An absolute value function, f, is graphed such that y = f(x). Which of the following is an equation for the function?

• y = |x|

• y = x^2

• y = x + 2

• y = 2x - 3