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![Greatest Integer
Function
Types of Functions
If a function f: R→ R is
defined by f(x) = [x], x ∈
X, round-off it to the
integer less than the
number. Suppose that the
given interval is in the
form of
(x, x+1), the value of
greatest integer function is
x which is an integer.](https://image.slidesharecdn.com/module2evaluatingfunctions-241214060748-10ca11a9/85/MODULE-2-Evaluating-Functions-and-Word-Problems-pptx-15-320.jpg)
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MODULE 2 (Evaluating Functions and Word Problems).pptx
- 1. General Mathematics Quarter 1– Module 2: Evaluating Functions
- 2. After going throughthis module, you are expected to: 1. recall the process of substitution; 2. identify the various types of functions; and 3. evaluate functions.
- 3. Means replacing the variablein the function, in his case x, with a value from the function’s domain and computing for the result. To denote that we are evaluating f at a for Evaluating Functions 1. Replace each letter in the expression with the assigned value. 2. Perform the operations in the expression using the correct order of operations.
- 4. A constant functionhas 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). Constant Function Types of Functions y=7
- 5. The identity function returnsthe same value and uses as its argument. It can be expressed f(x)= x, for all values of x. Identity Function Types of Functions f(2)= 2
- 6.
- 7. Linear Function Types ofFunctions y= 2x + 5 The polynomial function with degree one. It is in the form y= mx + b.
- 8. Quadratic Function Types of Functions Ifthe degree of the polynomial function is two, then it is a quadratic function. It is expressed as , where a ≠ 0 and a, b, c are constant and x is a variable.
- 9. Cubic Function Types ofFunctions A cubic polynomial function is a polynomial of degree three and can be denoted by , where a ≠ 0 and a, b, c, and d are constant & x is a variable. 5
- 10. Power Function Types ofFunctions A power function is in the form where b is any real constant number. Many of our parent functions such as linear and quadratic functions are functions.
- 11. Rational Function Types of Functions Arational function can be represented by a rational fraction say, in which numerator and denominator are polynomial functions of x, where q(x) ≠ 0.
- 12. Exponential function Types of Functions Thisfunction is in the form ,where x is an exponent and a and b are constants. (Note: only b is raised to the power x; not a.) If the base b is greater than 1, then the result is exponential growth.
- 13. Logarithmic Function Types of Functions Logarithmicfunctions are the inverses of exponential functions and vice versa. 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
- 14. Absolute Value Function Types ofFunctions The absolute value of any number, c, is represented in the form of |c|. If any function f: R→ R is defined by ,it is known as absolute value function. For each non-negative value of x, f(x) = x and for each negative value of x, f(x) = -x, i.e., f(x) = x, if x ≥ 0; – x, if x < 0.
- 15. Greatest Integer Function Types ofFunctions If a function f: R→ R is defined by f(x) = [x], x ∈ X, round-off it to the integer less than the number. Suppose that the given interval is in the form of (x, x+1), the value of greatest integer function is x which is an integer.
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