Answer to Question #236708 in Algebra for Lara

Question

Let g(x) be the transformation of f(x)= x2. Write the rule for g(x) using the change described.

1. compression vertically by a factor of 0.5 followed by a reflection

across the x-axis and a vertical shift 3 units down. _____________

2. horizontal stretch by a factor of 3, vertical compression by a factor of 1/3 followed by a horizontal shift right 5 units. ___________

Answer 1

1.

$$g(x)=-0.5x^2-3$$

2.

$$g(x)=3(\dfrac{1}{3}(x-5))^2$$