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Practice

4.11.7 Practice

4.11.7 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

For questions 1 - 3, use the graph below.

This graph shows four functions on an x, y coordinate plane. The \(x\)-axis runs from negative 8 to 9. The \(y\)-axis runs from negative 8 to 8. The first shows the decreasing function h of x = negative 2 times x plus 2. It passes through the points (0, 2) and (1, 0). The second is an increasing function that shows f of x = 2 times x plus 3. It passes through the points (0, 3) and (-1.5, 0). The third is an increasing function that shows j of x = 2 times x minus 6 and passes through the points (0, -6) and (3, 0). The fourth line is an increasing function where g of x = x divided by 2 minus 4 and passes through the points (0, -4) and (2 ,0).

  1. Tell the shift from j ( x ) = 2 x − 6 to f ( x ) = 2 x + 3 .
  1. Up 8
  2. Up 9
  3. Down 8
  4. Down 3
  1. Tell the transformations from f ( x ) = 2 x + 3 to h ( x ) = − 2 x + 2 .
  1. Vertical stretch, left 1
  2. Vertical stretch, right 1
  3. Vertical reflection, down 1
  4. Vertical reflection, up 1
  1. Describe the transformations made from the parent linear function to achieve g ( x ) = 1 2 x − 4 . Select two that apply:
  1. Vertical stretch of 1 2
  2. Vertical compression of 1 2
  3. Up 4
  4. Down 4
  5. Right 4
  6. Left 4
  1. What are the equations of the two lines shown?
    This graph shows two lines on an x, y coordinate plane. The \(x\)-axis runs from negative 4 to 6. The \(y\)-axis runs from negative 3 to 8. The first line has the equation y = -3 times x divided by 2 plus 1. The second line has the equation y = -3 times x divided by 2 plus 7. The lines do not cross.

    Select two that apply:

  1. y = x + 4
  2. y = x − 4
  3. y = − 3 2 x + 1
  4. y = 3 2 x − 7
  5. y = 3 2 x + 1
  6. y = − 3 2 x + 7
  1. The linear function f ( x ) = x has a vertical stretch of 3, a vertical reflection, and a vertical shift down 4. Which of the following is the new function?
  1. f ( x ) = − 3 x − 4
  2. f ( x ) = 3 x − 4
  3. f ( x ) = − 3 x + 4
  4. f ( x ) = 3 x + 4
  1. The linear function f ( x ) = x has a vertical compression of 1 3 and a vertical shift up 2. Which of the following is the new function?
  1. f ( x ) = 2 x − 1 3
  2. f ( x ) = 2 x + 1 3
  3. f ( x ) = − 1 3 x + 2
  4. f ( x ) = 1 3 x + 2
  1. What is the equation of the function graphed?

    This graph shows a linear function graphed on an x y coordinate plane. The x axis is labeled from negative 2 to 8 and the y axis is labeled from negative 1 to 8. The function f is graph along the points (0, 7) and (4, 4).

  1. y = − 4 3 x + 7
  2. y = − 3 4 x + 7
  3. y = 3 4 x + 7
  4. y = 3 x + 7
  1. The linear function f ( x ) = x has a vertical compression of 1 3 and a vertical shift down 2. Which of the following is the new function?
  1. f ( x ) = 2 x − 1 3
  2. f ( x ) = 2 x + 1 3
  3. f ( x ) = − 1 3 x − 2
  4. f ( x ) = 1 3 x − 2
  1. Which two transformations can be used to obtain the graph of g ( x ) = − ( x − c ) from the graph of g ( x ) = x ?
  1. A translation to the left c units followed by a reflection across the y -axis
  2. A translation to the right c units followed by a reflection across the y -axis
  3. A translation to the left c units followed by a reflection across the x -axis
  4. A translation to the right c units followed by a reflection across the x -axis
  1. For the functions h and g , which statement is true if h ( x ) = g ( x + 14 ) − 12 ?
  1. The graph of h is the result of the graph of g being translated left 14 units and up 12 units.
  2. The graph of h is the result of the graph of g being translated right 14 units and up 12 units.
  3. The graph of h is the result of the graph of g being translated left 14 units and down 12 units.
  4. The graph of h is the result of the graph of g being translated right 14 units and down 12 units.
  1. Which type of transformation can be used to obtain the graph of g ( x ) = 4 ( 2 + x ) from the graph of f ( x ) = 2 + x ?
  1. Vertical stretch
  2. Vertical shift up
  3. Vertical shift down
  4. Vertical shrink or compression