MAT-140 at Southern New Hampshire University emphasizes the algebra and concepts of functions. The catalog lists linear, polynomial, rational, trigonometric, exponential and logarithmic functions and says the course is intended for students who want to prepare for calculus.
The pace is quick because each family of functions has its own graph shape and rules. Students do best when they treat functions as relationships to understand, not formulas to memorize.
Course at a Glance
| Item | Details |
|---|---|
| University | Southern New Hampshire University |
| Course code | MAT-140 |
| Credits | 3 |
| Level | Undergraduate |
| Prerequisite | MAT-136, or a passing Math Alignment Score |
| Leads to | MAT-225 Calculus I (MAT-140 or MAT-142 is its prerequisite) |
| Typical work | Problem sets on graphs, transformations and equations (general; check your term) |
What MAT-140 Covers
| Function family | Key idea |
|---|---|
| Linear and polynomial functions | Slope, intercepts, zeros, end behavior |
| Rational functions | Asymptotes, holes and sign analysis |
| Trigonometric functions | Unit circle, graphs and identities |
| Exponential functions | Growth and decay modeling |
| Logarithmic functions | Inverses of exponentials and their laws |
| Applications | Real-world problem solving using these functions |
Key Concepts Explained
Asymptotes of a Rational Function
For f(x) = (x + 1) / (x - 2), the denominator is zero at x = 2, giving a vertical asymptote there. As x grows large the ratio approaches 1, giving a horizontal asymptote y = 1.
Check: f(100) = 101/98, about 1.03, and f(-100) = -99/-102, about 0.97. Both values sit close to 1, as predicted.
Exponential and Logarithmic Equations
To solve 3^x = 20, take logarithms of both sides: x = ln 20 / ln 3, which is about 2.727. A logarithm answers the question, to what power must the base be raised?
The Unit Circle
On the unit circle, cosine is the x-coordinate and sine is the y-coordinate. At 30 degrees (pi/6 radians), sine is 1/2. Learning a handful of special angles unlocks most trigonometry questions.
Typical Assignments and How to Approach Them
| Assignment type | What it tests | How to approach it |
|---|---|---|
| Function analysis problems | Describing a function from its equation | List domain, intercepts, asymptotes and end behavior before sketching |
| Equation solving | Algebraic technique | Isolate the function first, then use the inverse; always check for extraneous solutions |
| Modeling problems | Using exponentials or logarithms in context | Define variables, choose the model, then interpret the answer with units |
| Trig tasks | Unit circle and identities | Draw the angle, find the reference angle, then fix the sign by quadrant |
Transformations in One Table
Graph transformations show up in every function family. Learn the pattern once and reuse it:
| Change to f(x) | Effect on the graph |
|---|---|
| f(x) + k | Shifts up by k |
| f(x - h) | Shifts right by h |
| -f(x) | Reflects over the x-axis |
| a f(x), a > 1 | Stretches vertically |
| f(bx), b > 1 | Compresses horizontally |
A Worked Transformation
Describe the graph of y = 2^(x - 1) + 3. Start from y = 2^x. Replacing x with x - 1 shifts the graph right by 1, and adding 3 shifts it up by 3. The horizontal asymptote moves from y = 0 to y = 3.
Check: At x = 0 the value is 2^(-1) + 3 = 3.5, so the y-intercept is 3.5. The curve rises quickly to the right and flattens towards y = 3 on the left.
A Decay Model
A substance with a half-life of 5 years starting at 100 grams follows A(t) = 100 (1/2)^(t/5). After 10 years that is 100 x (1/2)^2 = 25 grams. Reading the structure of the model before calculating helps you interpret every number.
A Trigonometry Checkpoint
The unit circle ties the course together. On the unit circle an angle of 60 degrees (pi/3 radians) has cosine 1/2 and sine equal to the square root of 3 over 2, so tan is the square root of 3.
| Skill | Quick test of understanding |
|---|---|
| Radians | Convert 180 degrees to pi radians and back |
| Special angles | Recite sine and cosine at 30, 45 and 60 degrees |
| Graphs | Sketch sine and state amplitude and period |
| Inverse functions | Explain why arcsine has a restricted range |
Where Students Get Stuck
- Extraneous solutions. Always substitute back into logarithmic and rational equations.
- Mixing degrees and radians. Check your calculator mode.
- Memorized formulas without meaning. Sketch the graph to see if the answer is reasonable.
- Inverse confusion. Remember that log and exponential functions undo each other.
Study Tips for MAT-140
- Make a one-page sheet of function families and their graphs.
- Practice the special angles daily until they are automatic.
- Plot at least a few points when a graph is unfamiliar.
- Redo every missed problem a week later.
How We Help with MAT-140
Send the problem set, the lesson notes and your attempts. A maths tutor can walk through each method, prepare fully worked solutions to study from, or check your working. For the course that follows, see the related MAT-225 page.
GradeEssays is independent and not affiliated with Southern New Hampshire University. Our work is a study and reference aid: use it to understand the method, then complete and submit your own work under SNHU's academic integrity policy.
Every order is written from scratch, comes with free revisions within the scope of your original request, and is refunded in full if it is late.
Get Ready for Calculus with MAT-140
Share your problem set. A maths tutor prepares worked solutions and explains the reasoning.
Start My MAT-140 HelpFree revisions · Full refund if late · Written from scratch for your order
Frequently Asked Questions
SNHU lists MAT-136 or a passing Math Alignment Score.
Linear, polynomial, rational, trigonometric, exponential and logarithmic functions.
MAT-140 or MAT-142 is a prerequisite for MAT-225 Calculus I, along with a placement or alignment requirement.
They cover similar pre-calculus ground at different universities, but they are separate courses with separate requirements.
Check your course instructions; tools vary by term.
Yes. We review the setup and each step and explain any corrections.