Transformations of Functions

Front

If the blue function is f(x)=x², then the red function must be. Options: g(x)=x²-5, g(x)=x²+5, g(x)=(x-5)², g(x)=(x+5)²

Back

g(x)=x²-5

Front

If the blue function is f(x)=√x, the red function must be

Back

g(x)=-√x

Front

Describe the transformation to f(x) that results in g(x)=f(x-1)-5.

Back

f(x) has been translated to the right one and down five.

Front

The blue function is the parent function f(x) = x³. Which of the following is the correct equation for the red function, g(x)? Options: g(x)=x³+1, g(x)=x³-1, g(x)=(x-1)³, g(x)=(x+1)³

Back

g(x)=(x-1)³

Front

Which transformation maps the graph of f(x) = x² to the graph of g(x) = (x + 4)²? Options: a reflection across the line x = -4, a reflection across the line y = -4, a translation shifting f(x) 4 units to the left, a translation shifting f(x) 4 units to the right

Back

a translation shifting f(x) 4 units to the left

Front

If the yellow curve has equation f(x)=x², what is the equation of the blue curve?

Back

f(x) = (x+c)²

Front

Transformations to the graph compared to y=√(x)?

Back

Shifted right 2, shifted up 3, and reflected over the x-axis

Front

Which equation below is a quadratic function translated up 5 units? Options: y = x² + 5, y = (x + 5)², y = 5x², y = -x² - 5

Back

y = x² + 5

Front

Which equation is an absolute value graph shifted right 5 units? Options: y = |x - 5|, y = |x + 5|, y = |x| + 5, y = -5|x|

Back

y = |x - 5|