Functions
Which of these represents a function?
A) (1, 2), (2, 3), (1, 4) B) (2, 1), (3, 2), (4, 3)
B
Find the slope of the line passing through (2, 3) and (4, 7).
m = 2
Write y = -4x – 3 in standard form.
4x + y = -3
What transformation occurs from y = x to y = x + 4?
Up 4
A car’s value is $20,000 and decreases $2,500 each year. Write an equation for the value V after t years.
V = -2,500(t) + 20,000
Evaluate f(4) if f(x) = 3x – 5.
7
A line has slope –⅔ and passes through (6, 1). Write the equation in slope-intercept form.
y = -2/3x + 5
Convert –x + y = 5 into slope-intercept form.
Describe how the line y = 2x + 5 changes to y = 2x – 3.
Shifted down 8
A loan starts at $2,000 and decreases by $150 per month. Write the equation and interpret the slope and y-intercept.
y = -150x + 2000.
slope = losing $150 per month
y-intercept: He started with $2,000 which was the loan given to him.
Given the function g(x) = –2x + 7, f(x) = x2 + 4 find g(–3) + f(4).
= 33
Determine whether the lines through (1, 7) & (4, 1) and (–3, 4) & (0, –2) are parallel, perpendicular, or neither.
1:m= -2
2: m = -2
Parallel
Convert y – 2 = 3(x + 1) into slope-intercept form. Identify the slope and y intercept (point form)
y = 3x + 5
m = 3
y int = (0,5)
Describe how y = x changes to y = –2x + 1 (reflection, stretch/compression, translation).
It was reflected, stretched, and translated up 1
You pay a $15 service fee plus $2.25 per hour to rent a bike. Write an equation for cost C(h). Then find C(5).
C(h) = 2.25(x) + 15
C(5) = $26.25
Two functions are defined as f(x)=3x+1 and g(x)=3x−4. Compare their graphs: same slope means what? What does the different intercept tell you?
Same slope = Parallel.
The intercept tells us that f(x) is 5 points higher than g(x).
Determine if the lines through (1, 0), (5, 16) and (1, –19), (–2, –7) are parallel, perpendicular, or intersecting.
1: m = 4
2: m = 4
Intersecting
Write 6x – 4y = 12 in slope-intercept form.
y = 3/2 x -3
Given y = ½x + 1, write the equation after translating the line up 2 units and reflecting it over the y-axis.
y = -1/2 x + 3
A taxi charges $5 for pick-up and $2.50 per mile. Write the equation, find the cost for 8 miles, and explain what the slope and intercept represent.
f(x) = 2.5 (m) + 5
f(8) = $25
Slope: he is charged $2.5 per mile.
Y-Intercept: He is charged 5$ as soon as he gets in the taxi.
The points (–4, 10), (0, 6), (2, 4) lie on a linear function h(x). Write the equation for h(x)and use it to find h(5).
h(x) = -1x+ 6
h(5) = 1
A line passes through (–4, 6) and (2, –3). Write the equation of this line in slope-intercept form.
y = -3/2 x + 0 or y = -3/2x
The line passes through (2, 5) and has a slope of –3. Write the equation in point-slope form, slope-intercept form, and standard form.
point slope: y-5= -3(x-2)
Slope intercept: y = -3x + 11
Standard form: 3x + y = 11
Given y = 3x – 4, write an equation that is reflected over the x-axis, stretched by a factor of 2, and shifted down 5 units.
y = 6x - 9
A moving company charges a flat fee of $75 plus $1.75 per mile driven. Another customer paid $122 for their move. Use your equation to determine how many miles the customer moved. Round to the nearest whole mile.
f(x) = 1.75 (m) + 75
f(x) = 122
122 = 1.75 (m) + 75
47 = 1.75(m)
Miles = 26.8 but round up to 27 miles.