Practice Test #1 MAT 110
(1) Fill out the table and graph the function
x | g(x)
-2 |
-1 |
0 |
1 |
2 |
(2) Find the distance and the midpoint between the two points (-2, 6) and (4, 8)
(3) Give the center and radius of the circle with equation , and graph the circle.
(4) Use the vertical line test to tell whether the graph is of a function or not: (yes, i ripped this from the internet)
(5) Evaluate the function
(a) g(2) (b) g(9)
(6) Give the domain of the function:
(a)
(b)
(c)
(7) An object is thrown upward from a balcony, and at time t seconds after being launched, it's height is given by . Find the maximum height reached by the object.
(8) Graph the translate of the function x2, x3, or |x|, as applicable.
(a) (b)
(9) Is the function symmetric with respect to the y-axis?
(a) f(x) = |x – 2| , (b) g(x) = 4 – x2
(10) Use the formula to find the difference quotient of the function
(11) Find the average velocity of the function on the interval [4,5]
(use the formula )
(12) The director of an alumni association for a small college wants to determine whether there is any type of relationship between the average amount of an alumnus's contribution (in dollars) and the years the alumnus has been out of school.
Years | 1 5 3 10 7 6
Contribution| 500 100 300 50 75 80
(a) Find the linear regression equation y = ax + b for the data.
(b) Predict the amount in contributions for someone who had been out of the college for 8 years.
Solutions:
(1)
x | g(x)
-2 |
-1 |
0 | 2
1 | 3
2 | 10
(2) distance d =
midpoint =
(3) center (h, k) = (-4, 3) (note that if we're adding in the parentheses, the coordinate is negative),
radius:
(4) in order: yes, no, no, no
(5) (a) (b)
(6) (a)
This is a root function, set the radicand bigger or equal to zero:
(b) (b)
This is a rational function, so set the denominator equal to zero:
Then state the domain by extracting these numbers from the Reals:
, in interval notation:
(c)
This is a polynomial – it's domain is the entire set of real numbers:
(7) The graph of is a parabola (the square) facing downward (lead coefficient is negative), so the maximum would be at the vertex: So the maximum height achieve would be 396.56 feet.
(8) (a)
This will shift the graph of |x| (the 'arrowhead') 4 units to the right, and then the negative sign will reflect it across the x-axis (flip it):
(b)
This will shift the graph of the parabola x2 3 units left, and then 4 up:
(9) Graph 'em:
(a) (b)
no yes
(10)
(11)
(12) Use the TI-8x for this one – enter the top row as the x's in L1, and the bottom row in L2, then run the LinReg function as we did in class
The scatter plot: There is a negative relationship between the variables.
, The correlation coefficient is r = -.88, a pretty strong negative relationship between the years out of school and contributions.
About $49.66 would be my guess.