Question

Use the graphs of f and g to solve Exercises 87, 88, and 89.

87. Find the domain of f + g.
88. Find the domain of
`(f)/(g)`.
89. Graph f + g.

(You can just explain how to graph it for #89.)

Answer 1

87. [-4, 3]

88. (-4, 3)

89. See Attachment

General Formulas and Concepts:

Algebra I

• Reading a Cartesian Plane
• Coordinates (x, y)
• Functions
• Function Notation
• Domains - the set of x-values that can be inputted into a function f(x)
• [Interval Notation] - Brackets are inclusive, (Parenthesis) are exclusive

Explanation:

*Notes:

• When adding functions, the domain of the new function is defined as the intersections of the domains of f and g
• When dividing functions, the domain of the new function is defined as the intersections of the domains of f and g except for the points where g(x) = 0 (this is because we cannot divide by 0)

Step 1: Define

Identify the domains of each function.

Domain of f(x): [-4, 3]

Domain of g(x): [-5, 5]

Step 2: Find 87.

Determine the x-values for each function that overlap/intersect.

f(x) and g(x) have intersect from -4 to 3.

Domain f + g: [-4, 3]

Step 3: Find 88.

Determine the x-values for which g(x) = 0.

The function g(x) equals 0 at x = -4 and x = 3. Therefore, these x-values are excluded in the domain.

Domain of f/g: (-4, 3)

Step 4: Find 89.

To draw a graph of the f + g, we must combine the y-values for each x-value domain in a t-chart and plot by hand.

x | f(x) x | g(x) x | f + g

-4 5 -4 0 -4 5

-3 4 -3 1 -3 5

-2 3 -2 2 -2 5

-1 3 -1 2 -1 5

0 2 0 1 0 3

1 1 1 1 1 2

2 -1 2 1 2 0

3 -3 3 0 3 -3

Answer 2

Answers and explanations:

87. The domain of added functions includes the restrictions of both. So the range of the added function in this question is [-4, 3]

88. When finding the domain of a divided function we do the same as adding, but with an extra rule: g can't equal zero. So for this question the domain is (-4, 3)

89. To graph f + g you add the y-values for each x-value. I added a picture to help explain this one!