Exam Strategy

Readiness Check

You are ready when you can (1) write $b+mx$ from an arithmetic pattern, (2) write $ab^x$ from a geometric pattern, (3) use point forms $y_i+m(x-x_i)$ and $y_i r^{x-x_i}$, (4) diagnose tables by differences vs ratios, and (5) state domain differences between sequences and functions.

Prep Sequence

1. Ten table classifications (linear vs exponential). 2. Five sequence-to-function translations. 3. Five point-form builds. 4. Two domain contrast sketches. 5. Two-point determination for each family.

On the Exam

• Over equal intervals: constant Delta y => linear; constant ratio => exponential.
• Match additive language to $m$; multiplicative language to base $b$ or $r$.
• If the input is "year 0,1,2,..." as a sequence, say whole numbers; if any real time is allowed, use a function domain.
• With two exact points, set up the system for $b,m$ or $a,b$.

Common Traps

• Fitting a line to proportional growth.
• Copying $a_n$ formula but claiming continuous domain without comment.
• Mixing $f(x)=ab^x$ with $f(x)=a+bx$.
• Forgetting the point-ratio exponent is $x-x_i$.

Quick Checklist

• [ ] Additive vs multiplicative identified
• [ ] Correct function form written
• [ ] Point form uses $(x-x_i)$ correctly
• [ ] Domain note when comparing to a sequence
• [ ] Two-point determination completed when asked