Written Assignment 1¶
Question 1¶
1. What linear function, y=f(x) has f(0) = 8 and f(7) = 14 ?
Question 2¶
2. If
Let’s find f(t+h)
And then substitute f(t+h) and f(t) into the equation
Question 3¶
3. Find all solutions to the equation
we know that
The equation is true when
is refused as it is not in the domain of which is . is accepted.
So for
Question 4¶
4. Sketch the graph of
- The domain is
as there is no restriction on the value of . - The range is
. as the term is always positive and is added to it. - The line
is the horizontal asymptote (colored blue in the graph below) as approaches the value of approaches .
Question 5¶
5. Sketch the graph of
- The domain is
as must be positive (as it is the argument of the logarithm function). - The range is
as the logarithm function can take any value. - The line
is the vertical asymptote (colored green in the graph below) as approaches the value of approaches .
¶
Question 6¶
6. Find the domain fo the function
The function is defined for all values of
So the domain is
Question 7¶
7. From the graph below, find what is f(-15) and for what numbers x is f(x)=0.
as the graph crosses the x-axis at . when and as the graph crosses the x-axis at and .
Question 8¶
8. Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.
- The graph is function as for each value of
there is only one value of . - The domain is
as there is no restriction on the value of . - The range is
as the value of is always between -1 and 1. - The graph crosses the x-axis 5 times each period. So the x-intercepts in the period shown in the graph are
. - Symmetry with respect to the y-axis as the graph is symmetric about the y-axis and origin.
- No symmetry with respect to the x-axis.
Question 9¶
9. Determine whether the function is even, odd, or neither.
a.
A function is even if
a.
b.
c.
Question 10¶
10. A cellular phone plan had the following schedule of charges: Basic service, including 100 minutes of calls is $20.00/month; 2nd 100 minutes of calls is $0.075/minute; additional minutes of calls is $0.10/minute.
a. What is the charge for 200 minutes of calls in one month?
- The first 100 minutes are included in the basic service ($20.00/month).
- The next 100 minutes are charged at
0.075 × 100 = 7.50$). - Thus, the charge for 200 minutes is
.
b. What is the charge for 250 minutes of calls in one month?
- The first 100 minutes are included in the basic service ($20.00/month).
- The next 100 minutes are charged at
0.075 × 100 = 7.50$). - The next 50 minutes are charged at
0.10 × 50 = 5.00$). - Thus, the charge for 250 minutes is
.
c. Construct a function that relates the monthly charge C for x minutes of calls?