Name __Answer Key___ Date ______Period ____
PAP Pop quiz
Match each equation with the name of the function. 9. The function f(x)=log10 x +2 is vertically stretched by a factor of 3, reflected in the y-axis, horizontally 1. y = ex C A. logarithmic parent function transformed 4 units to the left and vertically transformed 2.5 units up. What is the equation of the vertical 2. y = ln x B B. natural logarithm function asymptote of the transformed function? A y = 3 log -1 (x + 4) + 2.5 D x = 4 3. y = log x A C. natural base exponential function B y = 3 log -1 (x + 4) + 4.5 E x = - 4
5. A curve has equation y = f (x). The following transformations are applied to the curve in the C y = 3 log -1 (x + 4) + 8.5 F y = 4 given order: • a reflection in the x-axis For Exercises 10–12, use the graph below.
• a dilation of factor 3 from the x-axis • a translation of 3 units in the positive direction of the x-axis The equation of the resulting curve is: A y = –3 f (x) + 3 D y = –3 f (x – 3) B y = 3 f (–x) + 3 E y = f (3 (1 – x))
C y = f (3x – 3) + 3 F None of these 10. Which graph represents the function
y = log (x – 1)? 10
Select true or false for each of the following statements. A. Graph A C. Graph C (A) True (B) False
5. The domain of a transformed logarithmic function is B. Graph B D. Graph D always {x ∈ R}.
(B) False 11. Which graph represents the function y = log10 4x?
6. Vertical translations must be performed before A. Graph A C. Graph C vertical stretches/compressions.
B. Graph B D. Graph D (B) False
7. A transformed logarithmic function always has a horizontal asymptote. 12. Which graph represents the function 1 y = log10 x – 1? (B) False 2
8. The vertical asymptote changes when a horizontal A. Graph A C. Graph C translation is applied.
(A) True B. Graph B D. Graph D
13.
14. Match the function with its graph. log 1
15.
Change h from 1.5 to 6
16. What transformations would need to be applied to f(x) from #15 so the resulting function has an x – intercept of (1,0)? Answers will vary – (one possible answer: Apply transformations so it is the parent function because the parent function has an intercept of (1, 0). shift down 5, compress vertically by .5, reflect horizontally, compress horizontally by 4, shift left 1.5)