PRECALCULUS HONORS TEST REVIEW 2.5 Find all the zeros of
... Use the Rational Zero Test to list all possible rational zeros of f. ...
... Use the Rational Zero Test to list all possible rational zeros of f. ...
Relative minimum
... a relative minimum at a focal point: Step 1: Find the focal points of the graph to determine the intervals on which f(x) is increasing or decreasing Step 2: Choose an x-value in each interval to determine whether the function is increasing or decreasing within that interval Step 3: If f(x) switches ...
... a relative minimum at a focal point: Step 1: Find the focal points of the graph to determine the intervals on which f(x) is increasing or decreasing Step 2: Choose an x-value in each interval to determine whether the function is increasing or decreasing within that interval Step 3: If f(x) switches ...
PDF
... The exponent, m, may also be a rational number as long as its denominator (when the number is reduced to lowest terms) is odd. This is because if the exponent is a fraction with an even denominator (such as ½), the exponent indicates an even root. An even root of a negative number does not give a re ...
... The exponent, m, may also be a rational number as long as its denominator (when the number is reduced to lowest terms) is odd. This is because if the exponent is a fraction with an even denominator (such as ½), the exponent indicates an even root. An even root of a negative number does not give a re ...
Inverse Functions
... We can extend these ideas from numbers to functions. There is exactly one function h : R → R such that h(x) + f (x) = f (x) + h(x) = f (x), for all f : R → R. This function, the additive identity for functions, has the formula h(x) = 0, for all x ∈ R. The additive inverse of the function f is the fu ...
... We can extend these ideas from numbers to functions. There is exactly one function h : R → R such that h(x) + f (x) = f (x) + h(x) = f (x), for all f : R → R. This function, the additive identity for functions, has the formula h(x) = 0, for all x ∈ R. The additive inverse of the function f is the fu ...
The Exponential Function A. Theorem 1 B. Example 1: Compound
... The exponential function describes growth and decay. Compound interest is an example of growth. Radioactive decay is an example of exponential decay. Suppose we start with N0 radioactive atoms. We cannot say when any particular atom will decay. What we do know is the half-life, call it H, defined as ...
... The exponential function describes growth and decay. Compound interest is an example of growth. Radioactive decay is an example of exponential decay. Suppose we start with N0 radioactive atoms. We cannot say when any particular atom will decay. What we do know is the half-life, call it H, defined as ...
Functions
... Show that (fg) is one-to-one if g:AB and f:BC are both one-to-one. Proof: We must show that, x,yA, xy (fg)(x) (fg)(y). Let x,y be distinct elements of A. Then, since g is one-to-one, g(x) g(y). Now, since g(x) g(y) and f is one-to-one, then f(g(x)) = (fg)(x) f(g(y)) = (fg)(y). ...
... Show that (fg) is one-to-one if g:AB and f:BC are both one-to-one. Proof: We must show that, x,yA, xy (fg)(x) (fg)(y). Let x,y be distinct elements of A. Then, since g is one-to-one, g(x) g(y). Now, since g(x) g(y) and f is one-to-one, then f(g(x)) = (fg)(x) f(g(y)) = (fg)(y). ...
Exponential Functions
... If b is any positive number, then the expression bx designates exactly one real number for every real value of x. Therefore the equation f(x) = bx defines a function whose domain is the set of real numbers. Furthermore, if we add the restriction b 1, then any equation of the form f(x) = bx describ ...
... If b is any positive number, then the expression bx designates exactly one real number for every real value of x. Therefore the equation f(x) = bx defines a function whose domain is the set of real numbers. Furthermore, if we add the restriction b 1, then any equation of the form f(x) = bx describ ...
PDF
... • The predecessor function p inverts the successor function on non-zero inputs. That means hat p(x)=y iff x=0 and y=0 or if x=y+1. Based on this analysis we define the predicate Rp as Rp (x,y) ≡ (x=0 ∧ y=0) ∨ y+1=x. What remains to show is that this representation is in fact correct, that is that p( ...
... • The predecessor function p inverts the successor function on non-zero inputs. That means hat p(x)=y iff x=0 and y=0 or if x=y+1. Based on this analysis we define the predicate Rp as Rp (x,y) ≡ (x=0 ∧ y=0) ∨ y+1=x. What remains to show is that this representation is in fact correct, that is that p( ...
![[Part 2]](http://s1.studyres.com/store/data/008795852_1-cad52ff07db278d6ae8b566caa06ee72-300x300.png)
Full text
... A Niven number is a positive integer that is divisible by its digital sum. That is, if n is an integer and s(n) Niven number if and only if sin) ...
... A Niven number is a positive integer that is divisible by its digital sum. That is, if n is an integer and s(n) Niven number if and only if sin) ...