THE ANSWER TO THE SYSTEM OF EQUATIONS IS Y= 2FOR EXAMPLE, CONSIDER...

4. The answer to the system of equations is y= 2For example, consider the portion of the graphandx= 13.shown below. For how many values does f(x) = 3?Functions, Domain, and Range

5

Functionsare written in the form beginning with:

4

3

f(x) =

2

1

For example, consider the function f(x) = 3x– 8.

x

If you are asked to find f(5), you simply substitute the

–6

1

2

3

4

5

6

7

–5

–4

–3

–1

–2

–7

5 into the given function equation.f(x) = 3x– 8

y

becomesf(5) = 3(5) – 8When f(x) = 3, the yvalue (use the y-axis) willf(5) = 15 – 8 = 7equal 3. As shown below, there are five such points.In order to be classified as a function, the functionin question must pass thevertical line test. The verti-cal line test simply means that a vertical line drawnthrough a graph of the function in question CANNOTpass through more than one point of the graph. If thefunction in question passes this test, then it is indeed afunction. If it fails the vertical line test, then it is NOT afunction.All of the xvalues of a function, collectively, arecalled its domain. Sometimes, there are xvalues that areoutside of the domain, and these are the xvalues forwhich the function is not defined.

G e o m e t r y R e v i e w

To begin this section, it is helpful to become familiar with the vocabulary used in geometry. The list below definessome of the main geometrical terms. It is followed by an overview of geometrical equations and figures.

arc

part of a circumference

area

the space inside a two-dimensional figure

bisect

cut in two equal parts

circumference

the distance around a circle

chord

a line segment that goes through a circle, with its endpoint on the circle

congruent

identical in shape and size. The geometric notation of “congruent” is

.

diameter

a chord that goes directly through the center of a circle—the longest line you can draw in a circle

equidistant

exactly in the middle

hypotenuse

the longest leg of a right triangle, always opposite the right angle

line

a straight path that continues infinitely in two directions. The geometric notation for a line is AB

.

line segment

the part of a line between (and including) two points. The geometric notation for a line segment is

PQ

.

parallel

lines in the same plane that will never intersect

perimeter

the distance around a figure

perpendicular

two lines that intersect to form 90-degree angles

quadrilateral

any four-sided figure

radius

a line from the center of a circle to a point on the circle (half of the diameter)

ray

a line with an endpoint that continues infinitely in one direction. The geometric notation for a ray

is AB

.

tangent line

a line meeting a smooth curve (such as a circle) at a single point without cutting across the curve.

Note that a line tangent to a circle at point P

will always be perpendicular to the radius drawn to

point P.

volume

the space inside a three-dimensional figure