1a. (7, 4) and (1, 1)

**Since the slope is positive, the line would rise (left to right).**

1b. (-3, 4) and (2, -1)

**Since the slope is negative, the line would fall (left to right).**

1c. (-5, 3) and (-5, 2)

**The slope is undefined.**

**Since the slope is undefined, the line would be vertical.**

2a. Slope = 3/2 and passes through the origin.

**Point/Slope Form:**

**Slope/Intercept Form:**

2b. *x*-intercept = 4 and *y*-intercept
= -3

**Slope:**

**Point/Slope Form:**

**Slope/Intercept Form:**

2c. Passes through (3, 2) and is parallel to .

**Slope:**

**Slope of line parallel to this line would be m = 2.**

**Point/Slope Form:**

**Slope/Intercept Form:**

2d. Passes through (-1, -1) and is perpendicular to .

**Slope of line perpendicular to this line would be m = -2/5.**

**Point/Slope Form:**

**Slope/Intercept Form:**

3a.

**Slope/Intercept Form:**

**Slope and y-intercept:**

**Lining up the equation with the slope/intercept form we get**

**slope = m = 2/3**

3b.

**Slope/Intercept Form:**

**Slope and y-intercept:**

**Lining up the equation with the slope/intercept form we get**

**slope = m = -2**

3c.

**Horizontal line:**

**Slope and y-intercept:**

**Slope = m = 0**

3d.

**Vertical line:**

**Slope and y-intercept:**

**Slope = m = undefined**

4a.

**Slope of the parallel line: **

Since parallel lines have the same slope and
this is a vertical line, then the slope is undefined.

**Slope of the perpendicular line: **

Since vertical and horizontal lines are perpendicular
to each other and this is a vertical line, then the slope of the perpendicular
line in this case would be the slope of a horizontal line which would be
0.

4b.

**Slope of the parallel line: **

Since parallel lines have the same slope and
this is a horizontal line, then the slope is 0.

**Slope of the perpendicular line: **

Since vertical and horizontal lines are perpendicular
to each other and this is a horizontal line, then the slope of the perpendicular
line in this case would be the slope of a vertical line which would be
undefined.

5a. center (-2, 0) and *r* = 3

6a.

Lining up the equation with the standard form we get

**center = ( h, k)
= (0, -5)**

7a. {(-1, 2), (1, 3), (-1, 4), (2, 5)}

**Is this a function or not? **

Since the input value of -1 goes with two output
values, 2 and 4, this relation would not be an example of a function.

**Domain **

The set of all input values would be {-1, 1,
2}.

**Range **

The set of all output values would be {2, 3,
4, 5}.

7b. {(1, 1), (2, 2), (3, 3), (4, 4)}

**Is this a function or not? **

Since every first element (or input) corresponds
with EXACTLY ONE second element (or output), this relation would be an
example of a function.

**Domain **

The set of all input values would be {1, 2, 3,
4}.

**Range **

The set of all output values would be {1, 2,
3, 4}.

8a.

At this point we ask ourselves, would we get one value for *y* if you plug in any value for *x*?

Since the answer to that question is yes, that means by definition, *y* is a function of *x*.

8b.

At this point we ask ourselves, would we get one value for *y* if you plug in any value for *x*?

Since the answer to that question is no, that means by definition, *y* is NOT a function of *x*.

9a.

*f*(*a*):

*f*(*a + h*):

**Putting it all together we get:**

10a.

To find *f*(-5), we need to go to the piece
of the function that *x* = -5 would be under,
which would be the first one where *x *__<__ 1:

To find *f*(1), we need to go to the piece
of the function that* x* = 1 would be under,
which would be the first one where *x *__<__ 1:

To find *f*(3), we need to go to the piece
of the function that *x* = 3 would be under,
which would be the second one where *x *> 1.

11a.

**The domain would be all real numbers except -5 and 5.**

11b.

**The domain is all real numbers.**

11c.

**Domain is x > 2/5.**

12a. ; *x* = -3, -2, -1, 0, 1, 2, 3

**Domain**

Since the domain is the set all input values, it corresponds to the *x*-values
in this problem.

This means that the domain is .

**Range**

Since the range is the set all output values, it corresponds to the
y-values in this problem.

This means that the range is .

12b. ; *x* = -1, 0, 3, 8

**Domain**

Since the domain is the set all input values, it corresponds to the *x*-values
in this problem.

This means that the domain is .

**Range**

Since the range is the set all output values, it corresponds to the
y-values in this problem.

This means that the range is .

12c. ; *x* = 0, 1, 2, 3, 4, 5, 6

**Domain**

Since the domain is the set all input values, it corresponds to the *x*-values
in this problem.

This means that the domain is .

**Range**

Since the range is the set all output values, it corresponds to the
y-values in this problem.

This means that the range is .

12d. ; *x* = -3, -2, -1, 0, 1, 2, 3

**Domain**

Since the domain is the set all input values, it corresponds to the *x*-values
in this problem.

This means that the domain is .

**Range**

Since the range is the set all output values, it corresponds to the
y-values in this problem.

This means that the range is {*y* |* y* = 5}.

12e. ; *x* = -2, -1, 0, 1, 2

**Domain**

Since the domain is the set all input values, it corresponds to the *x*-values
in this problem.

This means that the domain is .

**Range**

Since the range is the set all output values, it corresponds to the
y-values in this problem.

This means that the range is .

13a.

**a) x-intercept**

Since the

**b) y-intercept**

Since the

**c) Functional Value**

Since the functional value correlates with the
second or *y* value of an ordered pair,
then the functional value at *x* = 5 is 4.

**d) Increasing**

Since a function is increasing in an interval
when it is going up left to right in that interval, this function is increasing
on the interval .

**e) Decreasing**

Since a function is decreasing in an interval
when it is going down left to right in that interval, this function is
increasing on the interval .

**f) Constant**

Since a function is constant in an interval when
it is horizontal in that interval, this function is constant on the interval .

14a.

This graph would pass the vertical line test, because there would not be any place on it that we could draw a vertical line and it would intersect it in more than one place.

**Therefore, this is a graph of a function.**

14b.

This graph would not pass the vertical line test because there is at least one place on it that we could draw a vertical line and intersect it in more than one place.

**Therefore, this is not a graph of a function.**

15a.

**Since ,
then it is an even function.**

15b.

**Since ,
then it is an odd function.**

16a. *f*(-14.321)

**-15 is the greatest integer that is less than
or equal to -14.321. **

Last revised on July 3, 2010 by Kim Seward.

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