Transformation of Functions (DSE Maths)

The blue function is the original function f(x).

Which function represents the red function?

• -f(x)

• f(-x)

• f(x) + 1

• f(2x)

The blue function is the original function f(x) = x³.

Which equation represent the red function g(x)?

• g(x) = x³+1

• g(x) = x³-1

• g(x) = (x-1)³

• g(x) = (x+1)³

If the yellow curve has equation f(x)=x²,

• Then the blue curve is f(x) = x² - c
• Then the blue curve is f(x) = (x+c)²
• Then the blue curve is f(x) = (x-c)²
• Then the blue curve is f(x) = x² + c

Tags

CCSS.8.F.A.1

CCSS.8.F.A.2

CCSS.8.F.B.5

CCSS.8.G.A.3

In the figure, the vertex of the function f(x) is (-4, 5).

If g(x) = f(x + 2) , what is the vertex of g(x)?

• (-2, 5)

• (-6, 5)

• (-4, 3)

• (-4, 7)

Describe the transformation of

y = f(x) = x²

to the new function

g(x) = -(x+5)²

• translation upwards by 5

  and reflection in x-axis

• translation downwards by 5

  and reflection in x-axis

• translation leftwards by 5

  and reflection in x-axis

• translation rightwards by 5

  and reflection in x-axis

Describe the transformation of

y = f(x)

to the new function

y = 3 f(x + 2)

• Translate leftwards by 2 and

  enlarge vertically by a factor of 3

• Translate rightwards by 2 and

  enlarge vertically by a factor of 3

• Translate rightwards by 2 and

  contract to 1/3 the original along the y-axis

• Translate leftwards by 2 and

  contract to 1/3 the original along the y-axis

Describe the transformation of

y = f(x) = x²

to the new function

g(x) = 4(x - 7)²

• Translate rightwards by 7 and

  enlarge 4 times the original along y-axis

• Translate leftwards by 7 and

  enlarge 4 times the original along x-axis

• Translate leftwards by 4 and

  enlarge 7 times the original along y-axis

• Translate rightwards by 4 and

  enlarge 7 times the original along x-axis

Describe the transformation of

y = f(x)

to the new function

y = - f(x + 6) - 10

• Reflect with respect to y-axis, and

  translate downwards by 10 and leftwards by 6

• Reflect with respect to x-axis, and

  translate upwards by 10 and leftwards by 6

• Reflect with respect to y-axis, and

  translate upwards by 10 and rightwards by 6

• Reflect with respect to x-axis, and

  translate downwards by 10 and leftwards by 6

Describe the transformation of

y = f(x)

to the new function

y = f(5x)

• Enlarge 5 times the original

  along the x-axis

• Enlarge 5 times the original

  along the y-axis

• Contract to 1/5 times the original

  along the x-axis

• Contract to 1/5 times the original

  along the y-axis

Suppose f(x) = (x-3)² + 5.

What transformations took place

from the original function f(x) = x² ?

• Leftwards by 3 and upwards by 5

• Rightwards by 3 and downwards by 5

• Leftwards by 3 and downwards by 5

• Rightwards by 3 and upwards by 5