**MAT-121: COLLEGE ALGEBRA**

**Written Assignment 3**

2 points each except for 5, 6, 9, 15, 16, which are 4 points each as indicated.

**SECTION 3.1**

**Algebraic**

For the following exercise, determine whether the relationship represents y as a function of x. If the relationship represents a function then write the relationship as a function of *x* using *f* as the function.

**x+y2=5**- Consider the relationship 7n-5m=4.
- Write the relationship as a function
*n*=*k*(*m*). - Evaluate
*k*(*5*). - Solve for
*k*(*m*) = 7.

- Write the relationship as a function

**Graphical**

- Given the following graph
- Evaluate
*f*(4) - Solve for
*f*(x) = 4

- Evaluate

**Numeric**

For the following exercise, determine whether the relationship represents a function.

- {(0, 5), (-5, 8), (0, -8)}

For the following exercise, use the function *f* represented in table below. (4 points)

**x**

-18

-12

-6

6

12

18

**f(x)**

24

17

10

3

-4

-11

-18

- Answer the following:
- Evaluate
*f*(-6). - Solve
*f*(*x*) = -11 - Evaluate
*f*(12) - Solve
*f*(*x*) = -18

- Evaluate

For the following exercise, evaluate the expressions, given functions *f*, *g*, and *h*:

*f(x)=4x+2*; g(x)=7-6x; h(x)=7×2-3x+6

- f(-1)g(1)h(0) (4 points)

**Real-world applications**

- The number of cubic yards of compost,
*C*, needed to cover a garden with an area of*A*square feet is given by*C*=*h*(*A*).- A garden with an area of 5,000 ft2 requires 25 yd3 of compost. Express this information in terms of the function
*h*. - Explain the meaning of the statement
*h*(2500) = 12.5.

- A garden with an area of 5,000 ft2 requires 25 yd3 of compost. Express this information in terms of the function

**SECTION 3.2**

**Algebraic**

For the following exercise, find the domain and range of each function and state it using interval notation.

**f(x)=9-2x5x+13**

**Numeric**

For the following exercise, given each function *f*, evaluate *f *(3), *f *(-2), *f *(1), and f (0). (4 points)

**Real-World Applications **

- The height,
*h,*of a projectile is a function of the time,*t,*it is in the air. The height in meters for*t*seconds is given by the function h(t)= -9.8t2+19.6t. What is the domain of the function? What does the domain mean in the context of the problem?

**SECTION 3.3**

**Algebraic**

For the following exercise, find the average rate of change of each function on the interval specified in simplest form.

**k(x)=23x+1**on [2, 2+h]

**Graphical**

For the following exercise, use the graph of each function to **estimate **the intervals on which the function is increasing or decreasing.

For the following exercise, find the average rate of change of each function on the interval specified.

- g(x)=3×2-23×3 on [1, 3]

**Real-World Applications**

- Near the surface of the moon, the distance that an object falls is a function of time. It is given by d(t)=1.6t2, where
*t*is in seconds and d(t) is in meters. If an object is dropped from a certain height, find the average velocity of the object from t = 2 to t = 5.

**SECTION 3.4**

**Algebraic**

For the following exercise, determine the domain for each function in interval notation. (4 points)

- f(x)=2x+5 and g(x)=4x+9, find f-g, f+g, fg, and fg

For the following exercise, use each set of functions to findg(f(h(x))). Simplify your answers. (4 points)

- f(x)=x3-3,g(x)=6-x, and h(x)=2x

**Numeric**

For the following exercise, use the function values for *f *and *g *shown in table below to evaluate each expression.

**x**

-8

-6

-4

-2

2

4

6

8

**f(x)**

15

8

9

6

3

-3

-6

-8

**g(x)**

-6

-1

3

7

11

15

-8

23

- fg(4)
- fg(-8)
- gf(-6)
- gf(8)

For the following exercise, use each pair of functions to findf(g(-1))andg(f(-1)).

- f(x)= -62x+5, g(x)= -x2+7

**Real-World Applications**

- The radius
*r*, in inches, of a spherical balloon is related to the volume,*V*, by the following:

r=33V4

Air is pumped into the balloon, so the volume after *t *seconds is given byV(t)=15+18t. Find the composite function *r(V(t))* and use it to answer the following questions. Round the results to the nearest hundredth of a second.

- At what exact time is the radius 10 inches?
- At what exact time is the radius 20 inches?
- At what exact time is the radius 30 inches?

**SECTION 3.5**

**Algebraic**

For the following exercise, write a formula for the function obtained when the graph is shifted as described.

- g(x)=x is shifted up 3 units and to the left 1 unit.

For the following exercise, describe how the graph of the function is a transformation of the graph of the original function *f*.

- y=f(x-5)-9

For the following exercise, determine the interval(s) on which the function is increasing and decreasing.

- h(x)=6(x-8)2+7

**Graphical**

For the following exercise, sketch a graph of the function as a transformation of the graph of one of the toolkit (basic) functions. State the transformation in words.

- f(x)=x-32+2

**Numeric**

For the following exercise, determine whether the function is odd, even, or neither.

- f(x)=(x+4)2

For the following exercise, write a formula for the function *f *that results when the graph of a given toolkit function is transformed as described.

- The graph of f(x)=x is reflected over the
*x*-axis, shifted vertically up 1 unit, horizontally compressed by a factor of 37.

**SECTION 3.6**

**Algebraic**

- Describe the situation in which the distance that point
*x*is from 18 is at least 13 units. Express this using absolute value notation.

For the following exercise, find the *x-* and *y-*intercepts of the graph of the function.

- f(x)=x+9-11

**Real-World Applications**

- A machinist must produce a circular metal brace that is within 0.001 inches of the correct diameter of 6.5 inches. Using
*x*as the diameter of the circular metal brace, write this statement using absolute value notation.

**SECTION 3.7**

**Algebraic**

For the following exercise, findf-1(x) for the function.

**f(x)= -2x-13**

For the following exercise, find a domain on which the function *f *is one-to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of *f *restricted to that domain.

- f(x)=x+112-14

**Graphical**

For the following exercises, use a graphing utility to determine whether each function is one-to-one.

- f(x)=x-32+6

**Numeric**

For the following exercise, evaluate or solve, assuming that the function *f *is one-to-one.

- If f(23)=32, find f-132.

**Real-World Applications**

- The area
*A*of a circle is a function of its radius given by A(r)=r2. Express the radius of a circle as a function of its area. Call this function r(A). Find r(64)and interpret its meaning.

**SECTION 4.1**

**Algebraic**

For the following exercise, determine whether the equation of the curve can be written as a linear function.

- x+6=4y-2

For the following exercise, find the slope of the line that passes through the two given points.

- (-3, 5) and (6, -11)

For the following exercise, find a linear equation satisfying the conditions, if possible.

*x*-intercept at (2, 0) and*y*-intercept at (0, 3)

For the following exercise, determine whether the lines given by the equations below are parallel, perpendicular, or neither.

- 3x+8y=12 and 15-8y=3x

For the following exercise, find the *x*– and *y*-intercepts of the equation.

- 3×5+79y=23

For the following exercise, use the description of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?

- Line 1: Passes through (2, 3) and (4, −1)

Line 2: Passes through (6, 3) and (12, 6)

For the following exercise, write an equation for the line described.

- Write an equation for a line perpendicular to p(t)= -11t+14 and passing through the point (−3, −1).

**Graphical**

For the following exercise, find the slope of the lines graphed.

For the following exercise, sketch a line with the given features.

- A y-intercept of (0, -7) and slope of 35

For the following exercise, sketch the graph of the equation.

- g(x)=2×3-12

**Real-World Applications**

- At noon, a waitress notices that she has $12 in her tip jar. If she makes an average of $2.25 from each customer, how much will she have in her tip jar if she serves
*n*more customers during her shift?

**SECTION 4.2**

**Algebraic**

For the following exercise, consider this scenario:

- The weight of a newborn is 7.25 pounds. The baby gains38of a pound a month for its first year.
- Find the linear function that models the baby’s weight,
*W*, as a function of the age of the baby, in months,*t*. - When did the baby weigh 9.875 pounds?
- What is the baby’s weight after 10.5 months?

- Find the linear function that models the baby’s weight,