Exponential Function Manipulation Quiz

The function h is given by h(x) = 5 * 3^(-x/2). What is the value of h(1)? A. -5√3 B. 1/√15 C. 5/9 D. 5/√3

D. 5/√3

The functions f and g are given by f(x) = 2^x and g(x) = 2^x * 2^a, where a > 0. Which of the following describes the relationship between the graph of f and the graph of g? A. The graph of g is a vertical translation of the graph of f by a units. B. The graph of g is a horizontal translation of the graph of f by a units. C. The graph of g is a vertical translation of the graph of f by —a units. D. The graph of g is a horizontal translation of the graph of f by —a units.

D. The graph of g is a horizontal translation of the graph of f by -a units.

The function m is given by m(x) = (36^(x/2)). Which of the following expressions could also define m(x)? A. 6^x B. 6*(6^x) C. 18^x D. 18*(36^x)

A. 6^x

The function k is given by k9x) = 9^x. Which of the following expressions also defines k(x)? A. 2^(3x) B. 3^(2x) C. 3^(3x) D. 3^(x/2)

B. 3^(2x)

The function f is given by f(x) = 2^x, and the function g is given by g(x) = f(x)/8. For which of the following transformations is the graph of g the image of the graph of f? A. A horizontal translation to the left 3 units ​B. A horizontal translation to the right 3 units ​C. A vertical translation up 1/8 unit ​​D. A vertical translation down 1/8 unit

B. A horizontal translation to the right 3 units

The function f is given by f(x) = 3^x. The function g is given by g(x) = (f(x))^b, where b < 0. Which of the following describes the relationships between the graphs of f and g? A. The graph of g is a combination of a horizontal dilation of the graph of f and a reflection over the x-axis. B. The graph of g is a combination of a horizontal dilation of the graph of f and a reflection over the y-axis. (C and D are omitted due to char limit)

B. The graph of g is a combination of a horizontal dilation of the graph of f and a reflection over the y-axis.