For the following exercises, for each pair of points, a. find the slope of the line passing through the points and b. indicate whether the line is increasing, decreasing, horizontal, or vertical.
and
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Calculus Volume 1 · 1.2 Basic Classes of Functions
Basic Classes of Functions: practice problems
28 problems from the book, with its answers. Check your working, or have any of them explained to you on the whiteboard.
Exercises 61
For the following exercises, for each pair of points, a. find the slope of the line passing through the points and b. indicate whether the line is increasing, decreasing, horizontal, or vertical.
and
Exercises 63
Exercises 65
Exercises 67
Exercises 69
Exercises 71
Exercises 73
Exercises 75
Exercises 77
Exercises 79
Exercises 81
Exercises 83
Exercises 85
Exercises 87
Exercises 89
Exercises 91
Exercises 93
Exercises 95
Exercises 97
Exercises 99
Exercises 101
Exercises 103
Exercises 105
Exercises 107
Exercises 109
Exercises 111
Review Exercises 319
Key terms · 17
- algebraic function
- a function involving any combination of only the basic operations of addition, subtraction, multiplication, division, powers, and roots applied to an input variable $x$
- cubic function
- a polynomial of degree 3; that is, a function of the form $f (x) = a x^3 + b x^2 + c x + d,$ where $a \ne 0$
- degree
- for a polynomial function, the value of the largest exponent of any term
- linear function
- a function that can be written in the form $f (x) = m x + b$
- logarithmic function
- a function of the form $f (x) = \log_b (x)$ for some base $b > 0, b \ne 1$ such that $y = \log_b (x)$ if and only if $b^y = x$
- mathematical model
- A method of simulating real-life situations with mathematical equations
- piecewise-defined function
- a function that is defined differently on different parts of its domain
- point-slope equation
- equation of a linear function indicating its slope and a point on the graph of the function
- polynomial function
- a function of the form $f (x) = a_n x^n + a_{n - 1} x^{n - 1} + \text{…} + a_1 x + a_0$
- power function
- a function of the form $f (x) = x^n$ for any positive integer $n \ge 1$
- quadratic function
- a polynomial of degree 2; that is, a function of the form $f (x) = a x^2 + b x + c$ where $a \ne 0$
- rational function
- a function of the form $f (x) = \frac{p (x)}{q (x)},$ where $p (x)$ and $q (x)$ are polynomials
- root function
- a function of the form $f (x) = x^{1 \text{/} n}$ for any integer $n \ge 2$
- slope
- the change in y for each unit change in x
- slope-intercept form
- equation of a linear function indicating its slope and y-intercept
- transcendental function
- a function that cannot be expressed by a combination of basic arithmetic operations
- transformation of a function
- a shift, scaling, or reflection of a function
Learn 1.2 on the whiteboard
The tutor teaches the whole section, drawing it out step by step and answering your questions as you go.
