Functions
Given f(x) = 3(x-5) + 2, find f(3).
What is f(3) = -4
What is 50?
What is 1.
What is the y-intercept for the following function in standard form:
y = 3x2 - 2x + 7?
What is (0,7)
Distribute: x(2x - 5) = ?????
2x2 - 5x
A student took 4 tests and earned the following scores:
85, 72, 93, and 81.
Find the mean for this data.
What is 82.75
If f(x) = 4x - 5 and
g(x) = - 2x + 15,
is f(3) < g(3)?
Yes! f(3) = 7 and g(3) = 9.
In a lab, 400 bacteria increase to 600 bacteria after one hour. What is the growth rate per hour for this type of bacteria?
What is 1.5.
Find the vertex of the quadratic function, below, in vertex form:
y = 2(x - 5)2 - 2
What is (5, -2)
Solve for x:
(3x - 1)(x - 8) = 0
x = 1/3 and x = 8
A junior tracked his soda consumption, in ounces, for 30 days and created the following five-number summary. What was his 3rd quartile data calculation for his study, in ounces?
{ 16, 24, 30, 64, 72}
What is 64 ounces.
What is the Domain of a Function?
What is the set of all inputs for a function.
A TikTok influencer has lost followers during the past week after they received some negative press. They began at 1500 followers and a week later, had only 1000 followers. What is the rate of decrease over that week?
1500*B = 1000, so the decay factor is .666.
Thus, the rate of decay is (1 -.666) or .334.
Does the following graph open up or down? How do you know?
y = -3(x - 1)2 + 9
Down. The -3 "a-value" orients it downward.
Factor:
x2 - 3x - 54
What is (x - 9)(x + 6)
What does an "r value" of -1 mean?
What is a perfect negative correlation. (All points are going downward and the line of best fit "fits" perfectly)
The equation m = 40g gives the distance in miles that a car traveled, m, using g gallons of gas. If Rita traveled 140 miles, how much gas did she use?
What is 3.5 gallons.
A ball is dropped from the roof of an 80 foot building. Thus, at bounce 0, the ball had a height of 80 feet. After hitting the ground, the ball rebounds to 60 feet (b=1), then drops to the ground and rebounds to 45 feet (b=2), etcetera. Given this pattern, how high will the ball be on its 5th rebound (b=5)?
What is 18.98 feet.
How does the function g(x) "transform" (or move) from the parent graph f(x) = x2 if g(x) = 4x2 - 5?
The graph moves down 5 units and is 4 times "skinnier" than x2.
Factor and solve:
10x2 + 9x + 2 = 0
(5x+2)(2x+1)=0
Thus, x = -2/5 and x = -1/2
A survey included 100 different students who live in Chicago. The following information was collected on a survey:
40 students said they prefer biking to walking to school. 65 students live more than 1.5 miles from school, the others live closer. 38 students said they prefer to walk and live more than 1.5 miles from school.
How many students prefer walking if they live less than 1.5 miles from school?
What is 22 students.
If p(2) = 13 and p(5) = -2, what is the average rate of change?
(13- -2)/(2 - 5) = 15/-3 = -5
If a person invests $1000 at 10% for 40 years, calculated once a year, how much will it be worth at the end of the 40 years if they calculate using the exponential function equation? (y=a*bt)
What is $45,259.26
True or false: The function f(x) (in standard form) is equivalent to the function g(x) (in factored form) if
f(x) = 3x2+5x +1 and g(x) = (3x + 1)(x + 1).
False. f(x) would need to be 3x2+4x+1 for this to be true.
Use the quadratic formula to solve the following quadratic:
4x2 + 10x - 8 = 0
x = -3.317 and x = .6637
A survey included 100 different students who live in Chicago. The following information was collected on a survey:
40 students said they prefer biking to walking to school. 65 students live more than 1.5 miles from school, the others live closer. 38 students said they prefer to walk and live more than 1.5 miles from school.
How many students prefer biking if they live less than 1.5 miles from school?
What is 13 students.