Common Mistakes

Algebra I · Honors Math · Introduction to exponential functions

Real mistakes students make on write and graph exponential functions—and how to catch and fix them.

Focus for this topic: Write and graph exponential functions from equations, tables, and contextual information.

Frequent mistakes

### 1. Confusing f(x) evaluation with solving f(x) = k

What it looks/sounds like: Substituting when they should solve, or solving when they should evaluate.

Why it happens: Function notation looks like multiplication, so the verb “find” is ambiguous.

How to fix: Say the job: “plug in” vs “solve for x,” then mark the equation accordingly.

### 2. Calling a non-function a function

What it looks/sounds like: Accepting a relation where one input has two outputs.

Why it happens: Vertical-line test or mapping diagrams are skipped.

How to fix: For each x, list outputs; if two appear, it is not a function.

### 3. Domain and range swapped

What it looks/sounds like: Reporting outputs as domain or inputs as range.

Why it happens: Students memorize words without tying them to axes.

How to fix: Say “domain = allowed inputs (x); range = outputs (y).” Check the graph.

### 4. Open/closed endpoint mistakes

What it looks/sounds like: Including an endpoint that is open on the graph (or excluding a closed one).

Why it happens: Endpoint dots are easy to misread under time pressure.

How to fix: Trace the endpoint: filled = included, open = excluded; write the interval to match.

### 5. Piecewise piece chosen incorrectly

What it looks/sounds like: Using the wrong formula for the x-interval given.

Why it happens: Students look at the first piece instead of the domain restriction.

How to fix: Underline the condition that contains the input, then evaluate that piece only.

How to avoid them

1. Restate what 5.3 asks in one sentence before computing. 2. Name the method or representation you will use. 3. Define variables with units before writing symbols. 4. Check one easy special case, diagram estimate, or unit/domain check after a long solution. 5. Ask: does this answer match the required form and the prompt?

Quick self-check

• [ ] I can name two mistakes for 5.3
• [ ] I can explain why one of those mistakes happens
• [ ] I can fix one wrong solution by naming the broken step
• [ ] I can check that my final form matches what the prompt asked

Related materials

• Parent Guide, Exam Strategy, and Study Guide for 5.3 (same folder)
• Review and practice-test tiers under this topic when present