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Pre‐Calculus – Unit 2
Unit 2 Corrective Assignment – Functions and Limits
Pre‐Calculus
- Do the following pairs of input and output
values represent a function:
ሺ0, 4ሻ, ሺ4,4ሻ, and ሺെ2,3ሻ? If they don’t, give a
specific reason why not.
- Your GPA is a function of the grades you earn
in each class. Identify the independent and
dependent variables.
- Use the graph to the right to approximate the
following values to the nearest tenth.
a. ݂
b. ݂ ሺ0ሻ ൌ
c. If ݂ ሺݔሻ ൌ െ2, then ൌ ݔ
d. If ݂
, then the possible value(s) of ݔ
are:
- If the dependent variable is the height from the ground in feet and the independent variable is the
amount of time in seconds that you have spent on a Ferris Wheel, write a sentence explaining the
meaning of ܪሺ105ሻ ൌ 62.
- Tell if each graph below represents a function.
a. b.
x
y
x
y
x
y
x
y
x
y
For 6 ‐9, name the basic function shown and write the equation****.
- Function
- Function
- Function
- Function
For 10 ‐11, identify the domain intervals where each function is increasing, decreasing, and constant. Use interval
notation.
- Inc: Dec: 11) Inc: Dec:
Constant: Constant:
For 12 ‐15, identify the domain and range of each function. Use both interval notation and inequality notation.
Domain:
Interval: ______________
Inequality: ____________
Range:
Interval: ______________
Inequality: ____________
Domain:
Interval: ______________
Inequality: ____________
Range:
Interval: ______________
Inequality: ____________
Domain:
Interval: ______________
Inequality: ____________
Range:
Interval: ______________
Inequality: ____________
Domain:
Interval: ______________
Inequality: ____________
Range:
Interval: ______________
Inequality: ____________
x
y
x
y
x
y
x
y
x
y
x
y
Answer Key to PC Unit 2 Corrective Assignment
- Function. 2) Independent: grades you earn in each class.
Dependent: GPA
a) 1 b) 1 c) 0.5 d) -2.8, -1.5, or 0.
After 105 seconds on the Ferris Wheel, your height from the ground is 62 feet.
a) Function
b) Not a function
- Greatest Integer;
݂ ሺݔሻ ൌ intሺݔሻ
- Logarithm; ݂
log ݔ
- Linear; ݂
- Sine; ݂
ሺݔሻ ൌ sin ݔ
- Inc: ሺെ4, െ3ሻ ∪ ሺെ2, 3ሻ
Dec: ሺെ3, െ2ሻ
Const: ሺെ∞, െ4ሻ ∪ ሺ3, ∞ሻ
- Inc: ሺെ4, െ3ሻ ∪ ሺ2, 3ሻ
Dec: ሺെ∞, െ4ሻ ∪ ሺെ3, െ1ሻ ∪ ሺ3, െ∞ሻ
Const: ሺെ1, 2ሻ
- Domain: ሺ0, ∞ሻ; ݔ 0
Range: ሾ0, 3ሻ; 0 ݕ൏ 3
- Domain: ሾെ2, 5ሻ; െ2 ݔ൏ 5
Range: ሾെ2, 3ሿ; െ2 ݕ 3
- Domain: ሺെ5, െ1ሿ ∪ ሺ2, ∞ሻ; െ5 ൏ ݔ െ
Range: ሺെ3, െ1ሿ; െ3 ൏ ݕ െ
- Domain: ሺെ5, െ3ሿ ∪ ሺെ2, ∞ሻ; െ5 ൏ ݔ െ
and ݔ െ
Range: ሾെ2, ∞ሻ; ݕ െ
- Nonremovable infinite discontinuity at ݔൌ െ3.
Removable discontinuity at ݔൌ െ2.
Nonremovable jump discontinuity at ݔൌ 3.
- a. 3 b. Does not exist c. 1 d. 2 e. െ2 f. െ
18) HA:
lim
௫→ିஶ݂
ሺݔሻ ൌ െ
lim
݂௫→ஶ
ሺݔሻ ൌ െ
VA:
lim
௫→ିଶ
݂ష
ሺݔሻ ൌ െ∞
lim
௫→ିଶ
݂శ
ሺݔሻ ൌ ∞
19) HA:
lim
௫→ିஶ݂
ሺݔሻ ൌ 3
lim
݂௫→ஶ
ሺݔሻ ൌ 3
VA:
lim
௫→ଵ
݂ష
ሺݔሻ ൌ ∞
lim
௫→ଵ
݂శ
ሺݔሻ ൌ െ∞
x -2.1 -2.01 -2.001 -2 -1.999 -1.99 -1.
f(x) -11.3 -110.3 -1100.3 Error 1099.7 109.7 10.
HA:
lim
௫→ିஶ݂
ሺݔሻ ൌ െ0.
lim
݂௫→ஶ
ሺݔሻ ൌ െ0.
VA:
lim
௫→ିଶ
݂ష
ሺݔሻ ൌ െ∞
lim
௫→ିଶ
݂శ
ሺݔሻ ൌ ∞
