Transform Function Reflect Translate

Write g(x) (dashed line) in terms of f(x) (solid line).

• -f(x + 3) + 3

• f(-x + 3) + 3

• -f(x + 3) - 3

• -f(x - 3) + 3

Describe the transformations necessary to transform the graph of f(x) (solid line) into that of g(x) (dashed line).

• compress vertically by a factor of 2

• compress horizontally by a factor of 1, translate up 2 units

• compress vertically by a factor of 2, translate left 2

• compress vertically by a factor of 2, translate up 3 units

Identify the parent function f(x) and write an equation for the function given.

• g(x) = |3(x + 2)|

• g(x) = |(1/3)(x - 2)|

• g(x) = |(1/3)(x)| - 2

• g(x) = |3(x - 2)|

Identify the parent function f(x) and write an equation for the function given.

• g(x) = x³ - 3

• g(x) = -(x - 3)³ 

• g(x) = -x³ + 3

• g(x) = -x³ - 3

Describe the translations necessary to transform the graph of f(x) into that of g(x).

• Translate up 4 units

• Translate right 3 units

• Translate down 4 units

• Translate left 3 units

• Translate left 4 units

Answer explanation

Vertex of f(x): (0, 0)

Vertex of g(x): (-3, -4)

From (0, 0) to (-3, -4), we must translate/shift/move left 3 AND down 4 units.

Match the equation to its description.

• Stretched by factor of 4 and left 4

• Compressed by factor of 4 and up 4

• Stretched by factor of 4 and up 4

• Compressed by factor of 4 and left 4

Match the description to its equation.
Reflected over the x-axis 
Stretched by a factor of 2

• A

• B

• C

• D

• 
• 
• 
• 

What happens to the graph of the quadratic function f(x) = x^2 when it is transformed by f(bx), and 0 < |b| < 1?

• It undergoes a vertical compression

• It becomes narrower

• It undergoes a horizontal stretch

• It undergoes a vertical stretch

Determine the equation for the red graph.

• g(x)=(x-3)²

• g(x)=x²-3

• g(x)=x²+3

• g(x)=3x²