Functions and Graphing: College Algebra Fall 2026

Exam 2

what is domain?

set of all x-coordinated

what is domain of (0,1), (2,3), (4,5)

{0,2,4}

what is range?

set of all y-coordinates

what is range of (0,1), (2,3), (4,5)

{1,3,5}

what is interval notation?

set of real numbers using starting and ending points

what is the domain and range of (0,1) and (2,3) in interval notation

domain→(0,2) range→(1,3)

what does a closed point on a graph mean?

< or equal to or > or equal to; [x,y]

what does an open point on a graph mean?

< or >; (x,y)

what is a relation?

set of ordered pairs

how do you know if a relation is a function?

all x-coordinates will be different

a relation is not a function if…

the equation has more than one value; ±

what represents an increase on an open interval?

f(x1) < f(x2)

what represents a decrease on an open interval?

f(x1) > f(x2)

what represent a constant on an open interval?

f(x1) = f(x2)

what is relative maxima?

the peak of a graph on y-axis

where is the relative maxima?

located at x-axis

what is relative minima?

the lowest point on y-axis

where is relative minima?

located at x-axis

what represents an even function?

f(-x) = f(x)

what happens to right side of equation for an even function?

the right side stays the exact same as the left side

what represents an odd function?

f(-x) = -f(x)

what happens to the right side of the equation of an odd function?

right side is complete opposite of left side

an even function is symmetric to…

the y-axis

an odd function is symmetric to…

the origin

how do you graph a piecewise function?

plug in the f(x) for you y, and the if statement for you x

what is the difference quotient of function f?

f(x-h) - f(x) where h does not equal 0

what is the slope formula?

m = y2 - y1 / x2 - x1

what is point-slope formula?

y - y1 = m(x - x1)

what is slope-intercept formula?

y = mx + b

what is the general form equation of slope-intercept?

Ax + By + C = 0

if two vertical lines are parallel…

they have equal slopes

if two vertical lines have undefined slopes…

they are parallel

if two lines perpendicular…

their product of slopes = -1

if horizontal line has a slope of 0…

it is perpendicular to the vertical line with an undefined slope

what is the average rate of change formula?

f(x2) - f(x1) / x2 - x1

constant function: f(x) = c

—-

identity function: f(x) = x

/

absolute value function: f(x) = IxI

V

standard quadratic function: f(x) = x²

U

square root function: f(x) = square root of x

r

standard cubic function: f(x) = x³

sideways S

cube root function: f(x) = cube root of x

S

what does the + mean in y = f(x) + c?

graph shifted up c units

what does the - mean in y = f(x) - c?

graph shifted down c units

what does the + mean in y = f(x+c)?

graph shifted left c units

what does the - mean in y = f(x-c)?

graph shifted right c unites

how does -f(x) reflect on a graph?

over the x-axis

how does f(-x) reflect on a graph?

across the y-axis

what does the c > 1 mean in function cf(x)?

stretches the graph by multiplying all y-coordinates by c

what does 0 < c < 1 mean in function cf(x)?

shrinks graph by multiplying all y-coordinates by c

what does c > 1 mean in function f(cx)?

shrinks graph by dividing all x-coordinates by c

what does 0 < c < 1 mean in function f(cx)?

stretches graph by dividing all x-coordinates by c

what numbers are excluded from a functions domain?

real numbers that cause division by zero and result in square root of a negative number

what is the composition of a function?

you plug in g(x) for x in f(x)

the domain of f is equal….

to the range of inverse f^-1

how do you find the inverse of function f?

replace f with y, then swap you x and y

what does the inverse equation for function f(x) = 4x - 7?

y = 4x - 7 → x = 4y - 7

if a horizontal line does not pass through a graph more than once it is….

an inverse function

what is the distance formula?

d = the square root of (x2 - x1)² + (y2 - y1)²

what is the midpoint formula?

(x1 - x2 / 2 , y1 - y2 / 2) → (x,y)

what is the standard equation formula of a circle?

(x-h)² + (y-k)² = r² where h and k are points on graph

what is the center and radius of the standard equation (x - 0)² + (y - 6)² = 10²?

center = (0,6) and radius = the square root of 10 → 100

what is the general form equation of a circle?

x² + y² + #x + #y + # = 0