Equations in Standard Form
Determine the x and y-intercepts for the function:
3x + y = 9
y-int: (0,9)
x-int: (3,0)
What is the slope of the line that contains the points
(−2, 6) and (4, −6)?
m=-2
Is the following a function:
{(-1, 2), (0, 0), (3, 5), (4, 6)}
Yes, as each x is going to one y
What is a domain? What is range?
Domain is the x values of a function, Range is the y values of a function?
Write the equation of a line in point-slope form for a slope of -2 through (4, -7).
y+7=-2(x-4)
Determine the x and y-intercepts of the following:
-5x + 4y = 12
x-int: (12/-5,0)
y-int:(0,3)
What is the slope of the line passing through the points (1, 4) and (6, -1)?
m=-1
Is the following a function:
{(-2, -1), (1, 5), (3, 2), (1, -2)}
No, as x=1 is going to 2 y values.
Where can you find a minimum or maximum value?
The minimum value is the lowest y-value, the maximum value is the highest y value
Write an equation in point-slope form for the function. A zero at -3 and a slope of 3
y-0=3(x+3)
Is the point: (5, 0) on the line -4x + 5y = 20?
NO, -20 is not equal to 20
When driving on a highway, Ian passed the 23 mile marker with 15 gallons of gas in the tank. When he passed the 73 mile marker, he had 12.5 gallons of gas left. What is the average rate of change during this time? Include units in your answer.
m=50/2.5 miles per gallon or m=20 miles per gallon
Find f(12) using the following function: f(x) = -5x – 12
Is the function y=-3x+5 increasing or decreasing?
The function is decreasing as the slope is negative
Write an equation in point-slope form for the function that passes through the points (2, -5) and (3, -4).
y+4=1(x-3) or y+5=1(x-2)
Angela is in a comic book store where they sell classic and new comic books.The classics are $5 each, and the new ones are $2. Let x represent the number of classic comic books and y represent the number of new comic books. Write an equation to represent her purchases if she has $15 to spend.
5x+2y=15
What is the slope between the points: (5,3) and (12,11)
Find g(5) given the function g(x) = -⅗ x + 2
g(5)= -1
What is the x and y-int of the function y=3x+6
Y-int: (0,6)
x-int: (-2,0)
Use the information in the given table to write a point slope equation
x f(x)
3 15
4 12
5 9
6 6
y-15=-3(x-3)
Circular tables seat 8 people and rectangular tables seat 10 people. Write an equation that models the number of tables that would seat 80 people.
80=8c+10r
During a hike, Alex reached the 15th checkpoint with 20 liters of water in his backpack. When he arrived at the 45th checkpoint, he had 14 liters of water left. What is the average rate of change of water in Alex's backpack during this hike? Include units in your answer.
m= 1/5 liter per check point
g(x) = x3, find g(-3)
g(-3)= -27
What transformations have occurred g(x) = -2f(x + 6), how did this effect the domain and range.
Transformations: Reflection over the x-axis, stretched by a factor of 2, moved to the left 6.
The domain has no effect, the range would be flipped to be negative values of the original range.
The racetrack charges an annual membership fee and an entry fee per race. One racer paid $76 for 3 races and another paid $124 for 7 races. Write a linear function that models the situation.
y-76=12(x-3)