Review the new concepts in each section of the chapter and try to relate the mathematical meaning to each of the given terms.
Term
Mathematical Meaning
A. growth factor
III
B. asymptote
II
C. logarithmic function
I
D. exponential equation
IV
Practice makes perfect
We are given various mathematical terms.
A.growth factor B.asymptote [0.5em]
C.logarithmic function [0.5em]
D.exponential function [0.5em]
We will use the given mathematical terms and decide which meaning corresponds to each of them.
Mathematical Term A
The general form of the exponential function is y=ab^x. If the parameters are such that a>0 and b>1, the function grows as x increases. This is why b is called the growth factor.
The growth factor is the value of b in y=ab^x, when b>1.
Therefore, term A matches with Meaning III.
Mathematical Term B
If a function approaches a line as the x- or y-values go to infinity or negative infinity, we say that this line is an asymptote of the given function.
An asymptote is a line that a graph approaches as x or y increases in absolute value.
Therefore, term B matches with Meaning II.
Mathematical Term C
When we swap the coordinates of the points in the graph of a logarithmic function, we obtain the graph of an exponential function. Therefore, these are inverse functions.
A logarithmic function is the inverse of an exponential function.
Therefore, term C matches with Meaning I.
Mathematical Term D
Let's recall that the general form of an exponential function is y=ab^x, where x is a variable in the exponent. When we consider a specific y-value, for example let y=10, we obtain an equation that we can solve for x.
10=ab^x
Such equations are called exponential equations. Option IV gives this same definition with a more general case.
An exponential function is an equation of the form b^(cx)=a, where the exponent includes a variable.
