test 2

Question 1

”/” on the graph, f(x) = x
domain and range = all real numbers

Answer 1

identity function

Question 2

• positive parabola (does NOT go below the x axis) f(x) = x squared
  domain = all real numbers
  range= y is greater than or equal to 0

Answer 2

squaring function

Question 3

like the sine function but it if were vertical instead/odd function, f(x) = x cubed
domain and range = all real numbers

Answer 3

cubing function

Question 4

*** - pattern basically looks like the heart star/diamond pattern,
f(x) = 1/x
domain and range are both NOT equal to zero

Answer 4

reciprocal function

Question 5

*** - pattern looks like the natural log function but instead it touches zero and doesn’t go below the x axis (looks like ln cut off)
domain and range are both greater than or equal to zero

Answer 5

square root function

Question 6

• “r” growth, does not go below x axis (but does start in the - x axis)
  f(x)= b to the xth power
  domain = all real numbers but the range is greater than zero

Answer 6

exponential function

Question 7

** looks like the square root function except it never touches zero and starts from the bottom right side of the y axis
f(x)= ln(x)
domain is greater than zero and the range is all real numbers

Answer 7

natural log function

Question 8

• • looks like the cosine function if it were zoomed out or the cubing function turned sideways
    f(x) = sin (x)
    domain = all real numbers
    range= -1< y < 1
    – –

Answer 8

sine function

Question 9

• • like if the sine function were zoomed in & the max is the y intercept at 1 (basically just the bump)
    domain and range same as sine (domain is all real numbers, y is less than or equal to 1 but greater than or equal to -1)
    f(x) = cos(x)

Answer 9

cosine function

Question 10

• V !!!!
  f(x) = |x|
  domain = all real numbers
  range= greater than or equal to 0

Answer 10

absolute value function

Question 11

• • stepping stairs (first dot is shaded, second is not for every line made)
    f(x) = int(x) = [x]
    domain= all real numbers
    range = Z (idk either)

Answer 11

greatest integer function

Question 12

• kind of looks like the square root or natural log function but it starts out in the negative x axis like the exponential function does and crosses the y intercept at 0.5
  domain= all real numbers
  range= 0 < y < 1

Answer 12

logistic function

Question 13

y axis symmetry looks like the x2 function.
f(-x) = f(x) –> even (-x,y) = (x,y) function

Question 14

origin symmetry = odd function (x3)
for all x, f(-x) = -f(x)

Question 15

if x is not in the domain of g, it must not be in the domain of f(g(x))
any x for which g(x) is not in the domain of f must not be in the domain of f o g
so these values must be excluded from the input x

Question 15

The domain of all compositions is the set of all x such that
x is in the domain of g and g(x) is in the domain of f.

The following values must be from the
input x:
* If x is not in the domain of g, it must not be in the domain of
* Any x for which g(x) is not in the domain of f must not be in
the of

Answer 15

domains of composition

Question 16

• no two ordered pairs have the same output component
• must pass both vlt and hlt

Answer 16

1-1 function

Question 17

you prove that a function f is 1-1 with the inverse function g if and only if
f(g(x)) = x in the domain of g and
g(f(x)) = x in the domain of f

Answer 17

you find the inverse of a graph by drawing a reflection

Question 18

y = af(x) (dilation is made to the Y VALUE)
- if # is bigger than 1 it’s a v stretch and if not it’s a shrink (x, .5y) VS (x, 3y)

Answer 18

vertical dilation

Question 19

y= f(bx) (dilation is made to the X VALUE)
- if # is bigger than 1 it’s a h shrink because you divide it by x/#) and if not it’s a h stretch (1/3x,y) VS (1/.3x, y)

Answer 19

horizontal dilation

Question 20

y= f(-x) reflects original over the y axis –> (-x, y )
y= -f(x) reflects original over x axis –> (x, -y)

Answer 20

reflections

Question 21

graph of y= f(|x|) shows EVEN SYMMETRY
graph of y= |f(x)| reflects the portion of the graph below the x axis across the x axis and leaves everything else unchanged