Transforming Parabolas

If f(x) = x², which function is the result of shifting f(x) 3 units left and 2 units down?

• g(x) = (x + 2)² - 3

• h(x) = (x - 2)² + 3

• j(x) = (x + 3)² - 2

• k(x) = (x - 3)² + 2

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

The function f(x) = |x| is multiplied by k to create the new function g(x) = k|x|. Which statement is true about the graphs of f(x) and g(x) if k = 1/2?

• g(x) is a reflection of f(x) over the y-axis.

• g(x) is a reflection of f(x) over the x-axis.

• g(x) is wider than f(x).

• g(x) is narrower than f(x).

Caitlin graphs the function f(x) = ax², where a is a positive integer. If Caitlin multiplies a by -2, when compared to f(x), the new graph will become

• narrower and open downward

• narrower and open upward

• wider and open downward

• wider and open upward

If the parent function of f(x) is p(x) = x², then the graph of the function f(x) = (x - k)² + 5, where k > 0, would be a shift of

• k units to the left and a move of 5 units up

• k units to the left and a move of 5 units down

• k units to the right and a move of 5 units up

• k units to the right and a move of 5 units down

Tags

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

Josh graphed the function f(x) = -3(x - 1)² + 2. He then graphed the function g(x) = -3(x - 1)² - 5 on the same coordinate plane. The vertex of g(x) is

• 7 units below the vertex of f(x)

• 7 units above the vertex of f(x)

• 7 units to the right of the vertex of f(x)

• 7 units to the left of the vertex of f(x)

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

Given the parent function f(x) = x², the function g(x) = (x - 1)² - 2 is the result of a shift of f(x)

• 1 unit left and 2 units down

• 1 unit left and 2 units up

• 1 unit right and 2 units down

• 1 unit right and 2 units up

Tags

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

When the function f(x) = 2x² is transformed into g(x) = 2(x - 3)² + 4, the vertex of g(x) is

• 3 units to the right and 4 units up from the vertex of f(x)

• 3 units to the left and 4 units down from the vertex of f(x)

• 3 units to the right and 4 units down from the vertex of f(x)

• 3 units to the left and 4 units up from the vertex of f(x)

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

If the function h(x) = -x² is reflected over the x-axis, the new function j(x) will be

• j(x) = x²

• j(x) = -x²

• j(x) = 2x²

• j(x) = -2x²

Tags

CCSS.HSF.BF.B.3

If the function f(x) = (x + 2)² is vertically stretched by a factor of 3, what is the new function g(x)?

• g(x) = 3x² + 2x

• g(x) = x² + 2x + 3

• g(x) = 3(x + 2)²

• g(x) = x² + 6x

Tags

CCSS.HSF.BF.B.3

What is the effect on the graph of f(x) = x² when it is transformed into the function g(x) = -2f(x)?

• The graph is reflected over the x-axis and stretched vertically by a factor of 2.

• The graph is reflected over the y-axis and stretched vertically by a factor of 2.

• The graph is reflected over the x-axis and compressed vertically by a factor of 2.

• The graph remains unchanged.