1st semester Flashcards
Domain of a function
The set of allowable inputs for a function.
Range of a function
The set of outputs resulting from the allowable domain of a function.
function
A dependence relationship where each input has exactly one output.
vertical asymptote
This is formed when: As the input approaches a constant, the function’s outputs approach infinity or negative infinity.
horizontal asymptote
This is formed when: As the input approaches infinity, the function’s outputs approach a constant.
exponential function
This function has outputs that change by a constant percent (ratio, factor) as x changes by a constant difference.
linear function
This function has a constant rate of change.
horizontal line
This function is constant.
concave up
The part of a graph where the rate of change is increasing.
concave down
The part of a graph where the rate of change is decreasing.
decreasing exponential function
An exponential function where the growth factor is between 0 and 1.
increasing exponential function
An exponential function where the growth factor is greater than 1.
average rate of change
The difference in the outputs divided by the difference in inputs over a given interval.
Given f(x) = ax, find f(b)
ab
Given f(x) = 3x + 2 + x, find f(2).
10
Find the inverse of f(x) = 2x + 3
f’(x) = (x–3)/2
If g(t) = n, what is g’(n)?
t
If h(t) is the height in feet of a ball at time t in seconds, interpret h(3) = 10.
The height of the ball at 3 seconds is 10 feet.
If h(t) is the height in feet of a ball at time t in seconds, interpret h’(8) =9.
At 9 seconds, the the height of the ball is 8 feet.
If the growth rate of an exponential function is 3.4% per year, what is the growth factor?
1.034
If the continuous growth rate of an exponential function is 5.9% per year, what is the “k” number in the formula?
0.059
If the decrease rate of an exponential function is 9.2% per year, what is the growth factor?
0.908
If the continuous decay rate of an exponential function is 3.45% per year, what is the “k” number in the formula?
-0.0345
If the growth factor of an exponential function is 1.075, what is the growth rate?
7.5%
If the growth factor of an exponential function is 0.63, what is the decay rate?
37%
In the formula for an exponential function y = ab^x, what is a?
the y-intercept; the “initial” amount when t = 0.
Common logarithm
the power of 10 that produces a given number
Natural logarithm
the power of e that produces a given number
log 10
1
ln e
1
log 100,000
5
ln e^2
2
log(ab)
log(a) + log(b)
ln(a/b)
ln(a) – ln(b)
log(b)^t
t•log(b)
log(10^x)
x
10^(logx)
x
one order of magnitude larger
10 times larger
two orders of magnitude larger
100 times larger
three orders of magnitude larger
1000 times larger
Domain of y = log(x)
{reals > 0}
Range of y = ln(x)
{all reals}
Domain of y = 2^x
{all reals}
Range of y = 2^x
{all reals > 0}
f(x) + 3 produces what transformation on f(x)?
up three units
f(x – 5) produces what transformation on f(x)?
right five units
2f(x) produces what transformation on f(x)?
stretch vertically by a factor of 2 AWAY from the x-axis
f(3x) produces what transformation on f(x)?
compression TOWARD the y-axis by a factor of 1/3.
–f(x) produces what transformation on f(x)?
reflection over the x-axis
f(–x) produces what transformation on f(x)?
reflection over the y-axis
functions with y-axis symmetry
even functions
functions with origin symmetry
odd functions
y = 4/3x – 12
the equation for a linear function with slope 4/3 and y-intercept at (0, -12)
y = 320•(1.034)^t
the equation for an exponential function with initial amount 320 and growth rate of 3.4% per unit of time
two lines with the same rate of change (slope)
parallel lines
two lines whose slopes are opposite reciprocals
perpendicular lines
f(3) = 20
the symbolic representation of “function f at 3 is 20” OR “an input of 3 into function f has an output of 20”
h(t) = 300
the symbolic representation of “function h at t is 300” OR “an input of t into function g has an output of 300”
If a function approaches infinity as x approaches 3, then the function has this type of asymptote.
vertical asymptote
If a function approaches 4 as x approaches infinity, then the function has this type of asymptote.
horizontal asymptote
The equation of a parabola (in vertex form) with vertex (b, 4)
y = a(x – b)^2 +4
∆Q/∆x
the formula for average rate of change over a given interval
Write log(3x) = 4 in exponential form.
10^4 = 3x
Write 5x = 10^(4y) in logarithmic form.
log(5x) = 4y
Simplify: log(3 – 7y)
This log expression is already simplified. No log properties apply.
(reverse question)
The set of allowable inputs for a function.
Domain of a function
(reverse question)
The set of outputs resulting from the allowable domain of a function.
Range of a function
(reverse question)
A dependence relationship where each input has exactly one output.
function
(reverse question)
This is formed when: As the input approaches a constant, the function’s outputs approach infinity or negative infinity.
vertical asymptote
(reverse question)
This is formed when: As the input approaches infinity, the function’s outputs approach a constant.
horizontal asymptote
(reverse question)
This function has outputs that change by a constant percent (ratio, factor) as x changes by a constant difference.
exponential function
(reverse question)
This function has a constant rate of change.
linear function
(reverse question)
This function is constant.
horizontal line
(reverse question)
The part of a graph where the rate of change is increasing.
concave up
(reverse question)
The part of a graph where the rate of change is decreasing.
concave down
(reverse question)
An exponential function where the growth factor is between 0 and 1.
decreasing exponential function
(reverse question)
An exponential function where the growth factor is greater than 1.
increasing exponential function
(reverse question)
The difference in the outputs divided by the difference in inputs over a given interval.
average rate of change
(reverse question)
ab
Given f(x) = ax, find f(b)
(reverse question)
10
Given f(x) = 3x + 2 + x, find f(2).
(reverse question)
f’(x) = (x–3)/2
Find the inverse of f(x) = 2x + 3
(reverse question)
t
If g(t) = n, what is g’(n)?
(reverse question)
The height of the ball at 3 seconds is 10 feet.
If h(t) is the height in feet of a ball at time t in seconds, interpret h(3) = 10.
(reverse question)
At 9 seconds, the the height of the ball is 8 feet.
If h(t) is the height in feet of a ball at time t in seconds, interpret h’(8) =9.
(reverse question)
1.034
If the growth rate of an exponential function is 3.4% per year, what is the growth factor?
(reverse question)
0.059
If the continuous growth rate of an exponential function is 5.9% per year, what is the “k” number in the formula?
(reverse question)
0.908
If the decrease rate of an exponential function is 9.2% per year, what is the growth factor?
(reverse question)
-0.0345
If the continuous decay rate of an exponential function is 3.45% per year, what is the “k” number in the formula?
(reverse question)
7.5%
If the growth factor of an exponential function is 1.075, what is the growth rate?
(reverse question)
37%
If the growth factor of an exponential function is 0.63, what is the decay rate?
(reverse question)
the y-intercept; the “initial” amount when t = 0.
In the formula for an exponential function y = ab^x, what is a?
(reverse question)
the power of 10 that produces a given number
Common logarithm
(reverse question)
the power of e that produces a given number
Natural logarithm
(reverse question)
1
log 10
(reverse question)
1
ln e
(reverse question)
5
log 100,000
(reverse question)
2
ln e^2
(reverse question)
log(a) + log(b)
log(ab)
(reverse question)
ln(a) – ln(b)
ln(a/b)
(reverse question)
t•log(b)
log(b)^t
(reverse question)
x
log(10^x)
(reverse question)
x
10^(logx)
(reverse question)
10 times larger
one order of magnitude larger
(reverse question)
100 times larger
two orders of magnitude larger
(reverse question)
1000 times larger
three orders of magnitude larger
(reverse question)
{reals > 0}
Domain of y = log(x)
(reverse question)
{all reals}
Range of y = ln(x)
(reverse question)
{all reals}
Domain of y = 2^x
(reverse question)
{all reals > 0}
Range of y = 2^x
(reverse question)
up three units
f(x) + 3 produces what transformation on f(x)?
(reverse question)
right five units
f(x – 5) produces what transformation on f(x)?
(reverse question)
stretch vertically by a factor of 2 AWAY from the x-axis
2f(x) produces what transformation on f(x)?
(reverse question)
compression TOWARD the y-axis by a factor of 1/3.
f(3x) produces what transformation on f(x)?
(reverse question)
reflection over the x-axis
–f(x) produces what transformation on f(x)?
(reverse question)
reflection over the y-axis
f(–x) produces what transformation on f(x)?
(reverse question)
even functions
functions with y-axis symmetry
(reverse question)
odd functions
functions with origin symmetry
(reverse question)
the equation for a linear function with slope 4/3 and y-intercept at (0, -12)
y = 4/3x – 12
(reverse question)
the equation for an exponential function with initial amount 320 and growth rate of 3.4% per unit of time
y = 320•(1.034)^t
(reverse question)
parallel lines
two lines with the same rate of change (slope)
(reverse question)
perpendicular lines
two lines whose slopes are opposite reciprocals
(reverse question)
the symbolic representation of “function f at 3 is 20” OR “an input of 3 into function f has an output of 20”
f(3) = 20
(reverse question)
the symbolic representation of “function h at t is 300” OR “an input of t into function g has an output of 300”
h(t) = 300
(reverse question)
vertical asymptote
If a function approaches infinity as x approaches 3, then the function has this type of asymptote.
(reverse question)
horizontal asymptote
If a function approaches 4 as x approaches infinity, then the function has this type of asymptote.
(reverse question)
y = a(x – b)^2 +4
The equation of a parabola (in vertex form) with vertex (b, 4)
(reverse question)
the formula for average rate of change over a given interval
∆Q/∆x
(reverse question)
10^4 = 3x
Write log(3x) = 4 in exponential form.
(reverse question)
log(5x) = 4y
Write 5x = 10^(4y) in logarithmic form.
(reverse question)
This log expression is already simplified. No log properties apply.
Simplify: log(3 – 7y)
