Math 169 Test 2

1. Give the equation (in slope-intercept form) of the line with given properties: (7 points each)
(a) passes through the points (5, 0) and (–1, 4)


(b) passes through the point (4, –2) and is perpendicular to the line
2x -5y =10
The given line can be written as
which has slope2/5 .
Our line , therefore, has slope -5/2 .


2. Find the domain of each of the following functions. Write answers in interval notation. (5 points each)
(a)


The first term yields
x ≠ 4 and the second term gives
x≠ 0
So, D =

(b)

The numerator gives that
.
The denominator gives
x ≠4 and x ≠ -2
So, D =

3. Give the domain and range (in interval notation) of the function having graph below. (8 points)


4. Simplify the difference quotient


for the function
. (8 points)


5. The point

(2, -3) is on the graph of

y = f (x). What is the corresponding point on the graph of
. (5 points)
We need to multiply the x – value by1/8 .
We need to multiply the y – value by -4 and then add 2.
So we get( 1/4, 14)

6. The graph of

y = f (x) is shown below. Sketch the indicated graphs . Be sure to show the location of
the specific points marked on the original graph . (7 points each)


7. Put the quadratic function
in the form

completing the square . (8 points)


8. Find an equation for the quadratic function having graph shown below. (7 points)


9. A projectile is launched into the air, and its height above the ground (in feet) after x seconds is given
by. What is the maximum height reached by the projectile, and when is this
height achieved? (8 points)
We find the vertex to answer these questions.
The max height is achieved when
seconds.
The max height is then given by
f (2.5) =142 feet.

10. The table below gives values for two functions, f and g. Find the indicated values. (4 points each)


11. Suppose

f (x) =1/2x
and
. Find a simplified formula for and give the domain of the
function

( ). (10 points)


Now, the domain of g is x ≠ 6.

The domain of the expression is x ≠ 2.

So, the domain of

() is