- The distance between the two points.
Answer: The distance is
.
- The midpoint of the two points.
Answer: The midpoint is
.
- An equation of the line between the two points.
Answer: An equation of the line is
.
- An equation of the circle whose diameter is the line between
the two points.
Answer: An equation of the circle is
- When does a function have an inverse?
Answer: A function has an inverse only when it is one-to-one, which means that no two elements in the domain of f(x) correspond to the same element in the range of f(x). - What is the relationship between the domain and range of a
function and the domain and range of its inverse?
Answer: The domain of f(x) is the range of its inverse, and the range of f(x) is the domain of its inverse. - The graphs of a function and its inverse are symmetric to what
line?
Answer: They are symmetric to the line y=x. - Restrict the domain of the function
so
that its inverse exists.
Answer: There is more than one possible answer. The biggest intervals which will work are either
,
or 
.
- If f(x) has an inverse, find
.
Answer:
.
, and
, find the following.
- Find (f+g)(x).
Answer:
- Find (fg)(x).
Answer:
- Find f(g(x)).
Answer:
.
Describe the difference in words.
- f(x)+3.
Answer: It is shifted up vertically by 3 units. - f(x-4).
Answer: It is shifted to the right by 4 units. - f(x+5)+6.
Answer: It is shifted up vertically by 6 units and shifted to the left by 5 units. - -f(x).
Answer: It is reflected across the x-axis. - 2f(x).
Answer: f(x) is stretched vertically: all values of y are doubled.
|
- Approximate the interval(s) where the function is increasing?
Answer: It is increasing on the intervals
.
- Approximate the interval(s) where the function is decreasing?
Answer: It is decreasing on the interval [0,2].
Answer: The inequality is only true when x=4, and when x=-5.