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Vocabulary
Solve for X
Next Step?
Fill in the Blank
Describe the Graph
100
The little subscript number that comes after the word "log" in a logarithmic expression.
What is the BASE of a logarithmic expression?
100
log base 2 of 5 = x. x = ? (Round answer to two decimal places as needed.)
What is 2.32?
100
log (base 2) [(2x + 8)(x +2)] = 4. Step 1 = ?
What is "convert to an exponential equation"?
100
To determine whether or not a function has an inverse, you must first determine whether or not the function is _____?
What is one-to-one?
100
This word is used to describe any graph which falls from left to right.
What is decreasing?
200
A function wherein each y-value corresponds to only one x-value, and each x-value corresponds to only one y-value.
What is a one-to-one function?
200
log 7 - log 3 = x. x = ? (Round answer to two decimal places as needed.)
What is 0.37?
200
2^x = 8. Step 1 = Rewrite 8 as 2^3. 2^x = 2^3. Step 2 = ?
What is "Drop the bases and set the exponents equal to one another"? Bonus Q: What would you do if you could not set the bases equal to one another?
200
1) When a logarithmic expression appears without a specified base (ex. log 5 = x), one can ALWAYS assume that the base is _____. 2) When a NATURAL logarithmic expression appears without a specified base (ex. ln 5 = x), one can ALWAYS assume that the base is _____.
What is 10? What is e?
200
The graph of this type of function passes both the vertical and horizontal line tests.
What is a one-to-one function?
300
The name and notation for the inverse function of f(x).
"f-inverse" and "f^-1(x)"?
300
2^(x + 4) = 8^(x – 6). x = ?
What is 11?
300
Find the inverse of the following equation: f(x) = 6x + 2. Step 1: Replace "f(x)" with "y". y = 6x + 2. Step 2: Switch x & y. x = 6y + 2. Step 3: ?
What is "solve for y"?
300
In a compound interest problem, an interest rate of 7%/yr would correspond to an r-value of ____, and a time period of 18 months would correspond to a t-value of ___.
What is .07 and 1.5?
300
The graphs of inverse functions are mirror images (reflections) of one another across this line.
What is the graph of y=x?
400
The word abbreviated as "P" in the Discrete Compound Interest Formula.
What is "principal"?
400
Find the present value that will grow to $45,000 if interest is 3.6% compounded monthly for 1 year.
What is $43,411.15?
400
Prove that the following function is 1:1. f(x) = -4x + 12. Step 1: Substitute "x" with "a" and "b", then set the two equations equal to one another. -4a + 12 = -4b + 12. Step 2?
What is "Solve to prove that a = b".
400
The inverse of a logarithmic equation is always going to be a(n) ______, and vice versa.
What is an exponential equation?
400
This graph is constantly increasing and has an asymptote at y = 0.
What is the graph of an exponential function?
500
The domains and ranges of these functions are swapped.
What are inverses?
500
x^(4/3) = 81. x = ?
What is +/- 27?
500
log(3x+1) + log 3 = log(8x+9). Step 1?
What is "isolate the variable"?
500
Every logarithmic function will pass through the points (1/a, -1), (1,0), and ____.
What is (a, 1)?
500
The equation of the line which is the vertical asymptote of every logarithmic function.
What is x=0?