Chapter 1 vocabulary

Section 1.1 Vocabulary

Exponential, logarithmic, Trigonometric, and inverse trigonometric function are known as Transcendental functions.

A linear function is an equation for a straight line and can be written in the form y = mx + b where m is the slope and b is the y-intercept equation

The Slope(m) of a nonvertical line represents the number of units the line rises or falls vertically for each unit of horizontal change from left to right.

y = mx + b is known as the slope intercept form of the equation of a line.

The point-slope form of the equation of a line that passes through the point (x 1, y 1 ) is y - y 1 = m(x - x 1 )

The general form for the equation of a line is Ax + By + C = 0 where A and B are not both zero

Two distinct lines are parallel if and only if their slopes are the same.

Two distinct lines are perpendicular if and only if their slopes are negative reciprocals of eachother.

Section 1.2 Vocabulary

Function- each member of the domain (x-values) is paired with EXACTLY one member of the range (y- values).

Function Notation: y = f(x) f is the name of the function y is the dependent variable, or output value x is the independent value, or input value

The Domain of a function is the set of all values( x- values/ inputs) of the independent variable for which the function is defined.

The Range of a function is the set of all values ( y- values/ outputs) assumed by the dependent variable.

The difference Quotient: f(x + h) - f(x), h ≠ 0 h

Section 1.3 vocabulary

The graph of a function f is the collection of ordered pairs (x, f(x)) such that x is in the domain of f

Vertical line test A set of points in a coordinate plane is the graph of y as a function of x iff no vertical line intersects the graph at more than one point.

A function f is increasing on an interval if, for any x 1 and x 2 in the interval, x 1 < x 2 implies f(x 1 ) < f(x 2 ).

A function f is Decreasing on an interval if, for any x 1 and x 2 in the interval, x 1 f(x 2 ).

A function f is constant on an interval if, for any x 1 and x 2 in the interval, f(x 1 ) = f(x 2 ).

A function value f(a) is called a relative minimum of f if there exists an interval (x 1, x 2 ) that contains a such that x 1 < x < x 2 implies that f(a) ≤ f(x)

A function value f(a) is called a relative maximum of f if there exists an interval (x 1, x 2 ) that contains a such that x 1 < x < x 2 implies that f(a) ≥ f(x).

A function whose graph is symmetric with respect to the y-axis is an even function. f(-x) = f(x)

A function whose graph is symmetric with respect to the origin is an odd function. f(-x) = -f(x)

Section1.4 Vocabulary

Vertical and Horizontal Shifts Let c be a positive real number. Vertical and horizontal shifts in the graph y = f(x) are as follows: 1. Vertical shift c units up h(x) = f(x) + c 2. Vertical shift c units down h(x) = f(x) – c 3. Horizontal shift c units right h(x) = f(x-c) 4. Horizontal shift c units left h(x) = f(x+c)

Reflections in the Coordinate axes Reflections in the coordinate axes of the graph y = f(x) are as follows: 1.Reflection in the x-axis h(x) = -f(x) 2.Reflection in the y-axis h(x) = f(-x)

Horizontal shifts, vertical shifts, and reflections are called rigid transformations because the shape of the graph is unchanged.

Nonrigid transformations change the shape of the graph.

A nonrigid transformation of the graph y = f(x) is represented by y=cf(x), where the transformation is a vertical stretch if c > 1

A nonrigid transformation of the graph y = f(x) is represented by y=cf(x), where the transformation is a vertical shrink if 0 < c < 1

A nonrigid transformation of the graph y = f(x) is represented by h(x) = f(cx). If c > 0 it is a horizontal shrink If 0 < c < 1 then it is a horizontal stretch

Section 1.5 Vocabulary

Arithmetic Combinations Sum: (f + g) (x) = f(x) + g(x) Difference: (f – g) (x) = f(x) – g(x) Product: (fg)(x) = f(x) g(x) Quotient (f/g) (x) = f(x) / g(x)

The composition of the function f with the function g is (f o g)(x) = f(g(x)) Note: The domain of (f o g) is the set of all x in the domain of g such that g(x) is in the domain of f

Section 1.6 Vocabulary

By switching the first and second coordinates of the ordered pairs of a function you can form the inverse function, which is denoted f -1 (x).

Definition of Inverse function Let f and g ve two functions such that f(g(x)) = x, for all x in the domain of g And g(f(x)) = x for all x in the domain of f Thus, g(x) is an inverse function of f(x), and g(x) Can be denoted as f -1 (x).

To have an inverse a function must be one-to- one, which means that no two elements in the domain of f correspond to the same element in the range of f

Finding a linear model to represent the relationship described by a scatter plot is called fitting a line to data.