### Descriptive Statements:

- Analyze a variety of patterns.
- Analyze the properties of relations and functions in multiple representations (e.g., tables, graphs, equations, words).
- Analyze direct and inverse proportional relationships.
- Determine the effects of transformations on the graph of a function or relation.

### Sample Item:

A hiker climbs uphill at a steady pace, rests at a scenic spot for a while, then continues at a slower pace
to the top of the hill. The hiker stops for lunch at the top, then decides to run down to the base of the hill.
Which of the following graphs best expresses the hiker's speed as a function of time?

Correct Response and Explanation (ShowHide)

**C. ** This question requires the examinee to analyze the properties of relations and
functions in multiple representations (e.g., tables, graphs, equations, words). The "steady pace" held
by the hiker reflects a constant speed over time; thus the first section of the graph is a horizontal line
(slope equals zero) at some constant value of speed. The hiker slows to a resting position with a speed
of zero, though time passes so the value for time continues to increase. The approach to the top of the hill
shows a positive slope, with increasing speed and time as the hiker resumes walking, but since the pace is
slower, the graph does not reach the previous level of speed. This pattern repeats when the hiker stops
for lunch, but the run to the base reflects a greater speed than was achieved on the initial climb.

### Descriptive Statements:

- Manipulate algebraic expressions, equations, and inequalities (e.g., simplify, transform, factor).
- Solve linear and nonlinear equations and inequalities.
- Connect appropriate algebraic notation to phrases and sentences.

### Sample Item:

### Descriptive Statements:

- Analyze the relationship between a linear equation or inequality and its representations.
- Solve systems of linear inequalities or equations with a variety of methods.
- Interpret the meaning of the slope and the
*y*-intercept in various contexts.
- Analyze a variety of real-world problems involving linear equations, systems, and inequalities.

### Sample Item:

### Descriptive Statements:

- Analyze relationships between multiple representations of a nonlinear equation or inequality.
- Solve a variety of real-world problems involving nonlinear equations and inequalities.
- Analyze function behavior in terms of limits, continuity, and rates of change.
- Apply concepts of calculus to solve problems in real-world situations.

### Sample Item:

If the limit of function *h*(x) equals a real number *k* as *x* goes to negative infinity, which of the
following is the equation of an asymptote of the graph of *h*(x)?

*x* = –*k*
*y* = –*k*
*x* = *k*
*y* = *k*

Correct Response and Explanation (ShowHide)

**D. ** This question requires the examinee to analyze function behavior in terms of limits, continuity, and rates of change. The situation described can be represented as . This means that as *x* approaches negative infinity, *h*(*x*) approaches but never reaches *k* and that *y* = *k* is a horizontal asymptote.