This document discusses different types of functions including: - Constant functions which always output the same value regardless of the input - Identity functions which output the same value as the input - Polynomial functions defined by sums of terms with variables raised to whole number powers - Rational functions which are fractions of polynomials - Power functions in the form of y = axb where b is the exponent - Exponential functions in the form of y = abx where b is the base and x is the exponent - Logarithmic functions which are inverses of exponential functions - Absolute value functions - Greatest integer functions which round values to the nearest integer It explains that evaluating functions involves replacing variables in the function with assigned

1. EVALUATING
FUNCTIONS

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10. Before we begin, let’s go back to the time when you first
encounter how to evaluate expressions. Do you still
remember?
Given the following expressions, find its value if x = 3.
1. x – 9
2. 3x + 7
3. x2 + 4x – 10
4. 2x2 – 6x + 26
5. 3x2 – 6
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11. Types of Function
Type of Function Description Example
Constant Function A constant function is a
function that has the same
output value no matter what
your input value is. Because
of this, a constant function
has the form f (x) = b, where b
is a constant (a single value
that does not change).
y = 7
Identity Function The identity function is a
function which returns the
same value, which was used
as its argument. In other
words, the identity function is
the function f (x) = x , for all
values of x.
f(2) = 2
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Polynomial Function A polynomial function is defined
by y = a0 + a1x + a2x +...+ an xn ,
where n is a non-negative integer
and a0 , a1 , a2 ,…, n ∈ R.
Rational Function A rational function is any function
which can be represented by a
rational fraction say,
𝑝(𝑥)
𝑞(𝑥)
in which
numerator, p(x) and denominator,
q(x) are polynomial functions of x,
where q(x) ≠ 0.
𝑓 𝑥 =
𝑥2 − 3𝑥 + 2
𝑥2 − 4
Power Function A power function is a function in the
form b y = axb where b is any real
constant number. Many of our
parent functions such as linear
functions and quadratic functions are
in fact power functions.
f (x) = 8x5

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Exponential function These are functions of the form: x
y = abx , where x is in an exponent
and a and b are constants. (Note
that only b is raised to the power
x; not a.) If the base b is greater
than 1 then the result is
exponential growth.
y = 2x
Logarithmic Function Logarithmic functions are the
inverses of exponential functions,
and any exponential function can be
expressed in logarithmic form.
Logarithms are very useful in
permitting us to work with very large
numbers while manipulating
numbers of a much more
manageable size. It is written in the
form
y = logbx x> 0, where b>0 and
b≠1.
y = log749

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Absolute Value Function
Greatest Integer Function If a function f: R→ R is defined by
f(x) = [x], x ∈ X. It round-off to the
real number to the integer less than
the number. Suppose, the given
interval is in the form of (k, k+1), the
value of greatest integer function is
k which is an integer.

15. Evaluating function is the process of determining the value of
the function at the number assigned to a given variable. Just
like in evaluating algebraic expressions, to evaluate function
you just need to a.) replace each letter in the expression with
the assigned value and b.) perform the operations in the
expression using the correct order of operations.
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16. TRY THIS!
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