Linear Functions
Discrete Functions
Continuous Functions
Linear Word Problems
100
What is the slope-intercept form of a linear function? Give its general equation.
y = mx + b
100
Which of these sets of ordered pairs represents a function? Explain briefly.
A) {(1,2), (2,3), (3,4)}
B) {(1,2), (1,3), (2,4)}?
A) is a function;
B) is not a function because input 1 maps to two outputs (2 and 3).
100
Is the graph of a linear equation considered continuous? Briefly explain.
Yes. The graph of a linear equation is a straight line with no breaks, so it is continuous for all real x.
100
A taxi company charges a base fare of $3 plus $2 per mile. Write a linear function for the cost C in terms of miles m.
C(m)=2m+3
200
For the line with equation y=3x−5, what is the slope and what is the y-intercept?
Slope: 3
y-int: -5
200
A table shows n → f(n):
x | y
0→5
1→8
2→11
3→14
Is this mapping a function? Explain using the definition of a function.
Yes — each integer input maps to exactly one output.
200
Explain in one sentence the graphical difference between continuous and discrete functions.
Continuous functions can be drawn without lifting your pencil, while discrete functions are several individual points.
200
A phone plan costs $25 per month plus $0.05 per text message. If a student sent 200 texts, how much is the monthly bill? Show the calculation.
Bill: 25+0.05(200)
= 25+10
= 35 → $35.
300
Write the equation of a line in point-slope form that has slope −1/2 and passes through the point (4,1).
y−1=−1/2(x−4)
300
Which of these sets of ordered pairs represents a function? Explain your answer.
A) {(0,1), (1,5), (2,9), (3,13)}
B) {(0,1), (1,5), (2,9), (2,10)}
Set A is a function (each input 0,1,2,3 has one output).
Set B is not a function because input 2 maps to two outputs (9 and 10).
300
Consider the function f(x)=2x+3 with domain all real numbers. Is this function continuous everywhere? Explain.
Yes, f(x)=2x+3 is continuous for all real x because it can be drawn without lifting your pencil.
300
A car travels at a constant speed of 60 km/h. Write a linear equation for distance d (km) after t hours and find the distance after 2.5 hours.
d(t)=60t
d(2.5)=60(2.5)
=150 km
400
Write the equation of a line in point-slope form that has slope 3/4 and passes through the point (8,−1).
y+1=3/4(x−8)
400
The relation between student ID number and student name in a class: is this a function? Explain.
Yes — student ID → name is a function because each unique ID maps to exactly one name.
400
Look at the graph shown. Use the graph to state the domain and range in both inequality notation and interval notation.
D: (-∞ ,∞ ) -∞ <x<∞
R: (-∞ ,∞ ) -∞ <y<∞
400
A student saves $15 per week and already has $40. Write a function S(w) for total savings after w weeks, then find after how many weeks the student will have at least $190.
S(w)=15w+40.
15w+40=190
⇒15w=150
⇒w=10 So at least 10 weeks.
500
Write the equation of a line in point-slope form that has slope −3 and passes through the point (−2,5).
y−5=−3(x+2)
500
Look at the graph of the discrete function below. State the domain and range in both inequality notation and set notation. Is this mapping a function? Explain briefly.
D: {-1,0,1,2,3} D: -1≤ x≤ 3
R:{1,2,3} R: 1≤ y≤ 3
500
Use the graph below to state the domain and range in both inequality notation and interval notation.
D: (-3, 8] -3 < x ≤ 8
R: (-4.5, 2.5] -4.5 < y ≤ 2.5
500
A smartphone depreciates in value linearly. Its value is $900 when new and depreciates $150 each year. Find the linear function V(t) giving value after t years, then predict the value after 2.5 years.
V(t)=900−150t
V(2.5)=900−150(2.5)
=525 dollars