University:
University of North Georgia
Course:
MATH 1113 | Precalculus
Academic year:

2024
Views:

279

Pages:

3
Author:

5CelestialChronicle

Pre-Calculus Section 2.4 Worksheet [Day 2] Name: Key Suppose the graph of f(x) is given. Describe the transformations that would be performed on f(x) to obtain the function. 1. y = f(x) + 3 vertical shift up 3 2. y = f(x + 3) horizontal shift left 3 3. y = -f(-x) - 2 reflection over y-axis vertical shift down 2 4. y = -2f(x) vertical stretch of 2 reflection over x-axis 5. y = (1/3)f(x - 3) horizontal shift right 3 vertical shrink of 1/3 6. y = f(5x) + 1 horizontal shrink of 1/5 vertical shift up 1 The graphs of functions f, g, and h are given. Use function f to find a formula for functions g and h. The graph of f(x) is given. Sketch the graphs of the given functions. 9. a) y = -f(x) b) y = f(2x) 10. a) y = f(-x) b) y = f(x) + 1 c) y = 1/2f(x) d) y = f(x+1) + 1 A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. 1 1. itprospt.com itprospt.com 11. f(x) = x³; shift left 1, stretch vertically by a factor of 3, shift up 1 g(x) = 3(x+1)³ + 1 12. f(x) = √x; stretch horizontally by a factor of 2, reflect over the y-axis g(x) = √(-1/2x) 13. f(x) = |x|; shrink horizontally by a factor of 1/3, shrink vertically by a factor of 1/5, shift down 7 g(x) = 1/5|3x| - 7 14. f(x) = x²; shift right 3, reflect over the x-axis g(x) = -(x-3)² Apply the given transformations to the graph. The parent functions are already drawn for you. 15. f(x) = -|x - 3| + 2 - reflect over x-axis - right 3 - up 2 16. f(x) = (x + 1)² - 4 - left 1 - down 4 17. f(x) = √(-x) + 2 - reflect over y-axis - up 2 The graph of a function defined for x ≥ 0 is given. Complete the graph for x < 0 to make a) an even function and b) an odd function. 18. a. [Image of an even function] b. [Image of an odd function] 19. a. [Image of an even function] b. [Image of an odd function] Determine whether the function is even, odd, or neither. 20. f(x) = x² + x f(-x) = (-x)² + (-x) = x² - x NEITHER 21. f(x) = x³ - x f(-x) = (-x)³ - (-x) = -x³ + x ODD 22. f(x) = 1 - √x f(-x) = 1 - √(-x) NEITHER 23. f(x) = x⁴ + x² + 2 f(-x) = (-x)⁴ + (-x)² + 2 = x⁴ + x² + 2 EVEN