Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

b. g (ƒ (2))

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

c. ƒ(g (4))

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

d. g(ƒ(5))

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

e. ƒ(ƒ(8))

Use the table to ev​​aluate the given compositions. <IMAGE>

g(ƒ(4))

Use the table to ev​​aluate the given compositions. <IMAGE>

g(h(ƒ(4)))

Use the table to ev​​aluate the given compositions. <IMAGE>

h(h(h(0)))

Use the table to ev​​aluate the given compositions. <IMAGE>

g(ƒ(h(4)))

Use the table to ev​​aluate the given compositions. <IMAGE>

ƒ(ƒ(h(3)))

Find the linear function whose graph passes through the point (3, 2) and is parallel to the line $y=3x+8$ .

Evaluating trigonometric functions Without using a calculator, evaluate the following expressions or state that the quantity is undefined.

cos (2π/3)

Yeast growth Consider a colony of yeast cells that has the shape of a cylinder. As the number of yeast cells increases, the cross-sectional area A (in mm²) of the colony increases but the height of the colony remains constant. If the colony starts from a single cell, the number of yeast cells (in millions) is approximated by the linear function N(A) - CₛA, where the constant Cₛ is known as the cell-surface coefficient. Use the given information to determine the cell-surface coefficient for each of the following colonies of yeast cells, and find the number of yeast cells in the colony when the cross-sectional area A reaches 150 mm². (Source: Letters in Applied Microbiology, 594, 59, 2014)

The scientific name of baker’s or brewer’s yeast (used in making bread, wine, and beer) is Saccharomyces cerevisiae. When the cross-sectional area of a colony of this yeast reaches 100 mm², there are 571 million yeast cells.

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x .

Evaluate h(g( π/2)).

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x .

Find h (ƒ (x)).

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x.

Find ƒ(g(h( x))).

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x.

Find the domain of g o ƒ.

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x.

Find the domain of ƒ o g.

Demand function Sales records indicate that if Blu-ray players are priced at $250, then a large store sells an average of 12 units per day. If they are priced at $200, then the store sells an average of 15 units per day. Find and graph the linear demand function for Blu-ray sales. For what prices is the demand function defined?

Evaluating trigonometric functions Without using a calculator, evaluate the following expressions or state that the quantity is undefined.

tan (15π/4)

Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.

{Use of Tech} ƒ(x) = 1/(x-5)

Evaluating trigonometric functions Without using a calculator, evaluate the following expressions or state that the quantity is undefined.

sec (7π/6)

The population of a small town was 500 in 2018 and is growing at a rate of 24 people per year. Find and graph the linear population function p(t) that gives the population of the town t years after 2018. Then use this model to predict the population in 2033.

Find the inverse function (on the given interval, if specified) and graph both $f$ and $f^{-1}$ on the same set of axes. Check your work by looking for the required symmetry in the graphs.

$f\left(x\right)=8-4x$

Taxicab fees A taxicab ride costs $3.50 plus $2.50 per mile for the first 5 miles, with the rate dropping to $1.50 per mile after the fifth mile. Let m be the distance (in miles) from the airport to a hotel. Find and graph the piecewise linear function c(m) that represents the cost of taking a taxi from the airport to a hotel m miles away.

Graphing equations Graph the following equations. 

c. x² + 2x + y² + 4y + 1 = 0

Graphing functions Sketch a graph of each function.

ƒ(x) = { 2x if x ≤ 1 , 3-x if x > 1

Piecewise linear functions Graph the following functions.

$f\left(x\right)=\{\begin{array}{c}3x-1\frac{}{},\text{ if }x\le 0\\ -2x-1,\text{ if }x>0\end{array}$

{Use of Tech} Launching a rocket A small rocket is launched v​​ertically upward from the edge of a cliff $80$ ft above the ground at a speed of $96$ ft/s. Its height (in feet) above the ground is given by $h\left(t\right)=-16t^2+96t+80$, where $t$ represents time measured in seconds.

a. Assuming the rocket is launched at $t=0$, what is an appropriate domain for $h$?

Find the inverse function (on the given interval, if specified) and graph both $f$ and $f^{-1}$ on the same set of axes. Check your work by looking for the required symmetry in the graphs.

$f\left(x\right)=x^2+4$, for $x\geq{0}$

Draining a tank (Torricelli’s law) A cylindrical tank with a cross-sectional area of $10$ m² is filled to a depth of $25$ m with water. At $t=0$ s, a drain in the bottom of the tank with an area of $1$ m²  is opened, allowing water to flow out of the tank. The depth of water in the tank (in meters) at time $t\geq{0}$ is $d\left(t\right)=\left(5-0.22t\right)^2$.

a. Check that $d\left(0\right)=25$, as specified.