Families of Graphs

Families of Graphs

3-2

Multiple Choice

Which equation below is a quadratic function translated up 5 units?

• y = x² + 5
• y = (x + 5)²
• y = 5x²
• y = -x² - 5

Multiple Choice

Which parent function matches the graph?

• y = |x|
• y = ∛(x)
• y = x²
• y = a⋅b^x

Multiple Choice

Match the equation to its description.

• Right 2 and up 2
• Left 2 and up 2
• Right 2 and down 2
• Left 2 and down 2

Multiple Choice

g(x)=f(x)+6
Describe the transformation to f(x) that results in g(x).

• f(x) has been translated up 6.
• f(x) has been translated down 6.
• f(x) has been translated to the right 6
• f(x) has been translated to the left 6

Multiple Choice

g(x)=f(x)-4
Describe the transformation to f(x) that results in g(x).

• f(x) has been translated down 4.
• f(x) has been translated up 4.
• f(x) has been translated 4 units the left
• f(x) has been translated 4 units to the right

Remember, when you shift a function:

• If you add or subtract outside the parentheses, such as f(x)=x and f(x) = x + 8, or f(x) = x² and f(x) = x² - 3, you shift up or down from the parent function.

• If you add or subtract inside the parentheses, such as f(x) = x² and f(x) = (x+3)², you shift left or right opposite of the sign. In this example, you'd shift left 3 units.

• If you multiply the function, you make stretch or compress.