Question 1. Let f(x) = x². Find a formula for a function g whose graph is obtained from f by the given sequence of transformations.

(1) vertical stretch by a factor of 3

(2) shift right 5 units

(3) reflect across the x-axis

Question 2. Suppose (1, -5) is on the graph of y = f(x). Find a point on the graph of the transformed function y = f(x - 3).

Question 3. Determine analytically if the following functions are even, odd, or neither.

a.f(x) = 3x⁴ - x² + 5b.f(x) = 5x - 3

Question 4. Find the equation of the line passing through the point (2, -2) and perpendicular to the line y = x - 1

Question 5. Find the equation of a line parallel to y = 5 and passing through the point (1, - 7).

Question 6. Find the average rate of change of the function f(x) = x ² - 5 over the interval [-3, 2].