Parent Functions and Transformations
Describe the transformation.
f(x) = |x| - 1
The graph is a translation 1 unit down of the parent absolute value function.
Write a function g(x) whose graph represents the indicated transformation of f(x).
f(x) = x; horizontal shrink by a factor of 1/3
g(x) = 3x
You ride your bike and measure how far you travel. After 10 minutes, you travel 3.5 miles. After 30 minutes, you travel 10.5 miles. Write an equation to model your distance. How far can you ride your bike in 45 minutes?
y=0.35x; 15.75
The solution to a system of three linear equations is called what?
An ordered triple
What is the domain and range for the parent function f(x) = |x|
Domain: all real numbers
Range: y >= 0
Describe the transformation.
f(x) = -3(x+3)2
The graph is a vertical stretch by a factor of 3 followed by a reflection in the x-axis and translation 3 units left of the parent quadratic function.
Write a function g(x) whose graph represents the indicated transformation of f(x).
f(x) = |x|; reflection in the x-axis followed by a translation 4 units left.
g(x) = -|x+4|
The table shows the numbers of ice cream cones sold for different outside temperatures (in degrees Fahrenheit). Do the data show a linear relationship? If so, write an equation of a line of fit and use it to estimate how many ice cream cones are sold when the temperature is 60°F.
Temperature, x 53 62 70 82 90
Number of cones, y 90 105 117 131 147
Yes; y = 1.5x + 12; 102 ice cream cones
Name the three types of solutions that a system of three linear equations can have.
one solution, infinitely many solutions, no solutions.
What is the end behavior of the parent function f(x) = |x|?
As x -> inf, f(x) -> inf
As x -> -inf, f(x) -> inf
Describe the transformation.
f(x) = 1/2x2
The graph is a vertical shrink by a factor of 1/2 of the parent quadratic function.
Write a function g(x) whose graph represents the indicated transformation of f(x).
f(x) = -3x + 4; translation 3 units down and a reflection in the y axis.
If x and y have a strong positive correlation, and y and z have a strong negative correlation, then what can you conclude about the correlation between x and z? Explain.
As x increases, y increases, so z decreases. Therefore, the correlation between x and z is negative.
A linear system in three variables has no solution. Your friend concludes that it is not possible for two of the three equations to have any points in common. Is your friend correct? Explain your reasoning.
no; It is possible for a point (x, y, z) to satisfy two equations but not the third.
What is the name of the region that is bounded by graphing the system of inequalities in a linear programming problem?
Feasible region
The table below show the total distance traveled by a space probe after x seconds. What type of function can you use to model the date? Estimate the distance traveled by the space probe after 1 minute.
time (seconds): 0 8 20 36 50
Distance (miles): 0 76 190 342 475
Linear; about 570 miles.
Write a function g(x) whose graph represents the indicated transformation of f(x).
f(x) = |x+1| - 2; vertical shrink by a factor of 1/2 followed by a translation 2 units up.
g(x) = 1/2 |x + 1| + 1
A set of data pairs has a correlation coefficient r = 0.3. Your friend says that because the correlation coefficient is positive, it is logical to use the line of best fit to make predictions. Is your friend correct? Explain your reasoning.
Your friend is incorrect. Because r = 0.3 is closer to 0 than 1, the line of best fit will not make good predictions.
Solve the system:
4x + 5y - 3z = 15
x - 3y + 2z = -6
-x + 2y -z = 3
(1,1,-2)
On homework #0, Linear programming, you had a choice board and can pick two problems to work on. How many problems did you have to choose from, or how many problems were on the choice board?
6
You are playing basketball with your friends. The height (in feet) of the ball above the ground t seconds after you take a shot is modeled by the function f(t) = -16t2 + 26t + 6.5.
a. What is the value of t when the ball is released from you hand?
b. How many feet above the ground is the ball when it is released from your hand?
a. 0; at the moment the ball is released, 0 seconds have passed.
b. 6.5; f(t) represents the height of the ball, find f(0)
The total cost of an annual pass for admission to a national park plus camping for x days can be modeled by the function f(x) = 20x + 80. A senior citizen pays $20 less than half of this price for x days. What is the total cost for a senior citizen to go camping for three days in the park?
$50
Write an equation of a line that is passing through the point (8, −5) and is perpendicular to the graph of y = −4x + 1?
y = 1 /4 x − 7
A school band performs a spring concert for a crowd of 600 people. The revenue for the concert is $3150. There are 150 more adults at the concert than students. How many of each type of ticket are sold?
STUDENTS - $3
ADULTS - $7
CHILDREN UNDER 12 - $2
200 student tickets, 350 adult tickets, and 50 children under 12 tickets
A relation with distinct points is called what?
Discrete