Which Model Fits?
A table shows:
x: 0, 1, 2, 3
y: 5, 8, 11, 14
Which type of function best models the data?
What is a linear function?
Describe the graph that represents a linear function with negative slope
what is a straight line decreasing from left to right?
A company charges a membership fee plus a monthly cost.
The total cost, C, in dollars, is modeled by:
C = 25m + 60
What does 60 represent?
What is membership fee?
The equation of a linear function q and a table for linear function r are shown:
q(x) = 2x − 1
Table for r(x):
x: 0, 1, 2, 3
r(x): −2, 4, 10, 16
Compares the slopes.
What is slope of q is 2, slope of r is 6?
What is r has the greater slope?
Makayla buys some tools. She creates exponential function V to predict the value of her tools after t years. She predicts her tools will have a value of $380 after 1 year and a value of $361 after 2 years. Which equation represents function V?
A. V (t) = 400(1 – 0.05)t
B. V (t) = 399(1 – 0.19)t
C. V (t) = 380(1 – 0.05)t
D. V (t) = 380(1 – 0.19)t
What is A?
A quantity starts at 100 and decreases by 20% each hour.
Which function represents this situation?
What is Exponential Decay?
Describe the graph that represents exponential growth
What is a curve increasing slowly then rapidly upward? Looks like a hockey stick.
A taxi company charges a flat fee plus $2.50 per mile.
The total cost is modeled by:
C = 2.50m + 4
What does 2.50 represent?
What is the cost per mile?
Diego graphs Function A: y = −3x + 5
Jacob graphs Function B: linear function that passes through (0, 5) and (1, 8)
Compare the functions.
What is Slope of B is 3, slope of A is −3 ?
What is Function B increases and Function A decreases?
What is Function A and B have a point of intersection at (0, 5)?
What is Function A and B have a y-intercept at 5?
What is Function B: y = 3x + 5?
Yendi buys blackberries and raspberries to make pies.
● Blackberries cost $8 per pound.
● Raspberries cost $9 per pound.
● Yendi can spend a maximum of $40.
Create an inequality to represent how many pounds of blackberries, b, and raspberries, r, Yendi can buy.
What is 8b + 9r ≤ 40 ?
A ball is thrown upward and its height over time is modeled by the equation f(x) = -16x2 + 24x.
Which type of function models this?
What is a Quadratic Function?
Describe the graph that represents y = (x − 2)² + 1
What is a parabola opening upward with vertex at (2, 1) ?
An artist earns a profit from selling y paintings. His profit, P, in dollars, is modeled with the given equation.
P = (200y + 23.25) – (10.53y)
His profit is the difference in the amount of money he earns from selling his paintings and the cost of making the paintings.
Which expression represents the cost of making y paintings?
What is (10.53y)?
Which function has the greater maximum value?
y = −(x − 1)² + 6
y = −(x + 3)² + 4
What is y = -(x - 1)2 + 6?
Which table could represent a quadratic function?
A. x| 0, 1, 2, 3
f(x)| 3, 9, 27, 81
B. x| 0, 1, 2, 3
f(x)| -2, -4, -6, -8
C. x| -1, 0, 1, 2
f(x)| 6, 5, 6, 9
D. x| -3, -2, -1, 0
f(x)| 7, 7, 7, 7
What is A?
x: −1, 0, 1, 2
f(x): 6, 3, 2, 3
Which type of function best models the data?
What is quadratic function?
Describe the graph that represents a system with no solution
What are parallel lines?
What are straight lines with the same slope?
What are straight lines that do not intersect?
A ball’s height over time is modeled by:
h(t) = −4.9t² + 20t + 2
What does the number 2 represent in context?
What is the initial height of the ball?
Function f is quadratic:
f(x) = −(x − 2)² + 6
Function g is linear with equation:
g(x) = 4x − 1
Compare the end behavior.
What is f(x) has a maximum at (2, 6) whereas g(x) has no maximum?
What is domain for f(x) and g(x) is all real numbers?
What is range for f(x) is all real numbers less than or equal to 6?
What is range for g(x) is all real numbers?
Five points are plotted in the first quadrant.
From the graph, points appear to be:
(0, 0.2)
(1, 0.1)
(2, 0.05)
(3, 0.025)
(4, 0.0125)
Which equation could represent the function?
A. f (x) = 0.2(1 – 0.1)x
B. f (x) = 0.2(1 – 0.5)x
C. f (x) = 0.1(1 – 0.05)x
D. f (x) = 0.1(1 – 0.25)x
What is B?
Jana describes a graph as "looking like a hockey stick."
What kind of function models this graph?
Exponential Function
Describe the slope of a vertical line.
What is undefined slope?
A company uses the equation c(t)=20,000(1.80)t to predict how much money they will have in t years. How much did the company start with?
$20,000
Barbara and Jah'nessa both deposit $5,000. Barbara gains simple interest with 5% interest every year. Jah'nessa puts $100 into her account each year. Who will have more in year 6? How much more?
Barbara will have $900 more in 6 years.
The equation of the absolute value function that has been stretched by a scale factor or 3, reflected, and translated 2 units right and 4 units down from the parent function y = |x|
What is y = -3|x - 2| - 4?