Exam 2: More on Functions

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin. - 18 x=|y| A) x -axis only B) Origin only C) x -axis, y -axis, origin D) y-axis only

Determine the domain and range of the function. - A) Domain: $(- \infty , \infty )$ Range: [-3,3) B) Domain: (-3,3]; Range: $( - \infty , \infty )$ C) Domain: $( - \infty , \infty )$ ; Range: (-3,3] D) Domain: $( - \infty , \infty )$ ; Range: (-3,3]

The given point is on the graph of y = f(x). Find a point on the graph of y = g(x). -g(x)=f(x-1)+3 ;(4,13) A) (5,10) B) (14,10) C) (5,16) D) (14,16)

For the pair of functions, find the indicated domain. - Find the domain of f/g A) B) (-6,6) C) D)

The graph of the function f is shown below. Match the function g with the correct graph. -g(x)= -f(x)- 3

Answer the question. -How can the graph of be obtained from the graph of A) Shrink it vertically by a factor of Shift it vertically 2 units downward. B) Shrink it vertically by a factor of Shift it horizontally 2 units to the left. C) Shrink it vertically by a factor of Shift it horizontally 2 units to the right. D) Stretch it vertically by a factor of 4 . Shift it vertically 2 units downward.

The given point is on the graph of y = f(x). Find a point on the graph of y = g(x). - $\left. g ( x ) = f - \frac { 1 } { 4 } x \right) ; ( 3 , - 4 )$

Write an equation for a function that has a graph with the given characteristics. -The shape of $f ( x ) = 8.8 | - x | + 7$ is reflected across the y -axis. This graph is then vertically stretched by a factor of 8.8. Finally, the graph is shifted 7 units downward.

Solve. -Elissa sells two breeds of dogs, Alaskan Malamutes and Great Pyrenees. She has 78 feet of fencing to enclose two adjacent rectangular dog kennels, one for each breed. An existing fence is to form One side of the kennels, as in the drawing below. Let x represent the measurement indicated. Express the total area of the two kennels as a function of x. Graph the function and from the graph determine the value of x, rounded to the hundredths place, that will yield the maximum area. A) 19.50 feet B) 13.17 feet C) 13.33 feet D) 13.00 feet

Given the function f, match the function g with a transformation of f. -f(x)= x2 - 7, g(x)= 25x2 - 7

Graph the function. -

For the pair of functions, find the indicated sum, difference, product, or quotient. - Find (f/g)(x)

The given point is on the graph of y = f(x). Find a point on the graph of y = g(x). - $g ( x ) = \frac { 1 } { 4 } f ( x ) ; ( - 4,20 )$

The graph of the function f is shown below. Match the function g with the correct graph. -g(x)= f(x)+ 1

Solve. -The number G of gears a machine can make varies directly as the time T it operates. If it can make 3000 gears in 6 hours, how many gears can it make in 4 hours?

Graph the equation. -

For the pair of functions, find the indicated composition. - $f ( x ) = 4 x ^ { 2 } + 3 x + 8 , g ( x ) = 3 x - 6$ Find $( g \circ f ) ( x )$ .

Find the requested function value. - $f ( x ) = 5 x + 1 , g ( x ) = - 2 x ^ { 2 } - 3 x - 4$ Find $( f \circ g ) ( - 5 )$ A) 106 B) -194 C) 116 D) -1084

Consider the functions F and G as shown in the graph. Provide an appropriate response. -Find the domain of FG. A) [-3,4] B) [-1,3] C) [-3,3] D) [-1,4]

For the pair of functions, find the indicated composition. - f(x)=4 x+15, g(x)=3 x-1 Find $( f \circ g ) ( x )$