Perform

Now that you’ve seen the variety of ways in which the SAT can test you on functions, try the following questions to check your understanding. Give yourself 3.5 minutes to tackle the following three questions. Make sure you use the Kaplan Method for Math as often as you can. Remember, you want to emphasize speed and efficiency in addition to simply getting the correct answer.

  1. A single oscillation of a sine wave that bounces vertically between negative one and positive one graphed on a coordinate plane, between X equals negative four and X equals four. The graph crosses the y-axis at zero comma zero, and crosses the x-axis at approximately X equals negative 3.14, X equals zero, and X equals positive 3.14. The lowest point on the wave, which occurs only once, is located at about negative 1.6 comma negative one, and the highest point, which also occurs only once, is located at about 1.6 comma one.

    The graph of a trigonometric function, h(x) = sin x, is shown above. Which of the following correctly depicts the transformations affected in  ?

    1. A single oscillation of a sine wave that bounces vertically between negative 4.67 and negative 3.33 graphed on a coordinate plane, between X equals negative four and X equals four. The graph crosses the Y-axis at zero comma negative four, but does not cross the X-axis.
    2. Two and a half oscillations of a sine wave that bounces vertically between negative 4.33 and negative 3.67 graphed on a coordinate plane, between X equals negative four and X equals four. The graph crosses the Y-axis at zero comma negative four, but does not cross the X-axis.
    3. A single oscillation of a sine wave that bounces vertically between negative 0.67 and positive 0.67 graphed on a coordinate plane, between X equals negative four and X equals four. The graph crosses the Y-axis at zero comma point 5, and crosses the x-axis three times.
    4. Two and a half oscillations of a sine wave that bounces vertically between negative 0.33 and positive 0.33 graphed on a coordinate plane, between X equals negative four and X equals four. The graph crosses the Y-axis at zero comma 0.25, and crosses the x-axis five times.

  2. Briana is writing a 60-page paper for a law school class; she has completed a full outline of the paper and needs to convert it to prose. She estimates that she will average 45 words per minute while typing. If one page of prose contains approximately 500 words, which of the following correctly estimates the number of prose pages, p, remaining as a function of the number of minutes, m, that Briana types?

  3. A scatterplot titled Speed versus fuel economy. Fuel economy, in miles per gallon, is plotted along the vertical axis from 20 to 44 in increments of 6. Speed, in miles per hour, is plotted along the horizontal axis from zero to 100 in increments of 25. The data first increases, reaches a maximum at approximately 50 comma 41, and then decreases. The data points are as follows: 5 comma 28, 10 comma 29, 15 comma 30, 20 comma 31, 25 comma 33, 30 comma 34, 35 comma 36, 40 comma 39, 45 comma 40, 50 comma 41, 55 comma 40, 60 comma 39, 65 comma 37, 70 comma 33, 75 comma 31, 80 comma 29, and 85 comma zero.

    The graph above shows a compact car’s fuel economy as a function of speed. Which of the following is true?

    1. The rate of increase in fuel economy below 50 mph is greater than the rate of decrease in fuel economy above 50 mph.
    2. The rate of increase in fuel economy below 50 mph is equal to the rate of decrease in fuel economy above 50 mph.
    3. Fuel economy peaks at 50 mph, but nothing can be said about the rates of change in fuel economy above and below 50 mph.
    4. The rate of increase in fuel economy below 50 mph is less than the rate of decrease in fuel economy above 50 mph.