Transformations

Which statement best describes the change from the linear parent function to the equation g(x) = 12x ?

• The graph of g is steeper than the linear parent function.

• The graph of g is less steep than the linear parent function.

• The graph of g was shifted down from the linear parent function.

• The graph of g was shifted up from the linear parent function.

Answer explanation

Multiplying by a number greater than one makes the graph more steep.

Describe the transformation of y = (x - 4)² from the function y = x²

• vertical shift up 4 units

• vertical shift down 4 units

• horizontal shift left 4 units

• horizontal shift right 4 units

Answer explanation

Subtraction inside parentheses.

Describe the transformation of y = x² + 4 from the function y=x²

• Horizontal shift right 4 units

• Horizontal shift left 4 units

• vertical shift up 4 units

• vertical shift down 4 units

Answer explanation

Addition outside of parentheses.

In the equation f(x)=5(x+3)²-10 how does the 10 transform the quadratic parent function?

• Vertical stretch by a factor of 10

• Vertical compression by a factor of 10

• Vertical shift down 10 units

• Vertical shift up 10 units

Answer explanation

The 10 was being subtracted outside of parentheses.

Pablo throws a ball with a path of

y = -5(x - 2)².

Maria throws a ball with a path of

y = -5(x - 2)² + 10.

Which description is reasonable for the difference in the two equations?

• Maria throws the ball 10 times harder than Pablo does.

• Maria starts her ball at a height 10 feet higher than Pablo does.

• Pablo throws the ball 10 times harder than Maria does.

• Pablo starts his ball at a height 10 feet higher than Maria does.

Answer explanation

Maria has +10 outside of parentheses compared to Pablo.

• The graph of f is shifted 6 units up to create the graph of g.

• The graph of f is wider than the graph of g

• The graph of f is shifted 6 units down to create the graph of g.

• The graph of f is more narrow than the graph of g.

Answer explanation

Subtraction outside of parentheses.

• There is a vertical shift down 3 units

• The parabola is reflected across the x-axis

• It causes the parabola to be more narrow

• It causes the parabola to be wider

Answer explanation

For transformations, anytime you multiply a negative number you reflect the graph across the x-axis.

What would the graph of y = 0.25x look like compared to the linear parent function? Draw it

Answer explanation

Multiplying by a number less than one creates a graph that is less steep (flatter)

Draw the graph of

h(x) = (x + 5)² + 3

Mark the vertex before drawing the curve.

Answer explanation

The vertex should be at (-3, 5). Addition inside parentheses shifts to the left, and addition outside parentheses shifts the function up.

Tags

CCSS.HSF-IF.C.7A