3-1 Relations and Functions
3-2 Linear Functions
3-3 Transforming Linear Function
3-4 Arithmetic Sequence
3-5 Scatter Plots and Lines of Fit
3-6 Analyzing Lines of Fit
3-6 Analyzing Lines of Fit
100
What is the definition of domain and what is the definition of the range of a function?
The domain is the set of x-values or inputs. The range is the set of y-value or outputs.
100
f(x) is another way to say...
y
100
What is a translation? And does the slope change if we translate a function?
A translation shifts every point of a function up, down, left or right. The transformed line will always have the same slope.
100
What is the deffinition of common difference?
The difference between any two consecutive terms that is constant.
100
When y-values tend to increase as x-values increase, the two data sets have what type of association.
Positive
200
What is the domain of the following set of data?
(3,5), (4,7),(5,9)
{3,4,5}
200
Evaluate when x = 4
f(x) = -2x + 9
1
200
Describe the transformation from f to g
f(x) = 2x + 2
g(x) = f(x) - 8
Shift down 8 units
200
Is this an example of an arithmetic sequence? If so, what is the common difference?
2,5,8,10,13, ...
No. There is no common difference.
200
A scatter plot where there is no general relationship between the x-values and y-values has what type of association?
No association
300
What is the range of the following set of data?
(4,-7), (5, -9), (6, -11)
{-7,-9,-11}
300
Evaluate for n = 5
f(n) = 2(n - 1)
8
300
Describe the transformation from f to g.
f(x) = -2x + 7
g(x) = -2(x + 4) + 7
A horizontal shift left 4 units
300
Is this an example of an arithmetic sequence? If so, what is the common difference?
18, 13, 8, 3, ...
Yes, -5
300
The trend line of a set of data is molded by the following function;
y = -2x + 5
What type of association does the set of data have, and why?
Negative, since the slope of the trend line is negative.
400
Is the relationship a function? If so, classify it!
Yes, it is many to 1.
400
Sketch the graph of
f(x)=1/2x+5
400
Describe the following transformation from f to g.
f(x) = 8x + 2
g(x) = 4x + 1
It is a VERTICAL compression with a scale factor of 1/2. The slope and y-intercept are scaled by a factor of 1/2.
400
What is the 5th term of the following arithmetic sequence?
3, 9, 15, 21, _____
27
400
What type of correlation does a line of best fit with an r value of -0.3216 have?
A weak negative correlation
500
What is the equation of the linear function represented by the data?
y=-2/3x+3
500
A periscope lens is sticking out of the ocean 24 inches above the waters surface.
a) If the periscope ascends at 6 inches per second, what function can model the situation? Use t for time. [ hint: f(t) = __________ ]
b) If the periscope reaches its maximum height at 22 seconds, what is the maximum height in feet?
a) f(t) = 6t + 24
b) f(22) = 156 inches, divided by 12 = 13 feet!
500
Given f(x) = 3x + 7, describe the transformation of
g(x)=x + 7. Explain.
It is a Horizontal stretch with an "a" value of 1/3.
The slope is scaled by 1/3 but the y-intercept stays the same,
500
What is the 45th term of the following arithmetic sequence?
3, 9, 15, 21, ...
267
500
a) Use technology to perform a linear regression to determine the equation if the line of best fit for the data.
b) Estimate the value of y when x = 15.
c) Does this have a strong or weak positive or negative correlation? Explain.
a) y = 1.55x+16.6
b) f(15) = 39.85
c) Strong positive correlation since r = .9943254636 and that is VERY close to 1.