Modded SAT Question Bank
by Abdullah Mallik dedicated to DPT SAT Batches and Someone Special | GitHub
We're excited to announce that we've launched a new and improved question bank with enhanced features and a more user-friendly interface.
To access the new question bank, please visit OnePrep.
We believe that this new platform will provide you with a better overall experience. Thank you for your continued support!
Test
Math
Domain
Advanced Math
Skill
Nonlinear functions
Difficulty
Medium
ID: d675744f
Modded SAT Question Bank by Abdullah Mallik

y equals, 4 times, open parenthesis, 2 to the x power, close parenthesis

Which of the following is the graph in the xy-plane of the given equation?

  1. The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 4 through 4, in increments of 1, are indicated on the x axis. The numbers negative 25 through 100, in increments of 25, are indicated on the y axis. The curve begins to the left of the y axis, high above the x-axis. As it moves rightward it goes downward, at first steeply, then more and more slowly as it gets closer and closer to the x axis. Eventually it goes downward toward the x axis so slowly it is almost horizontal. The curve passes through the point with coordinates negative 2 comma 32, and the point with coordinates negative 1 comma 8, and crosses the y-axis a little above the origin. It ends to the right of the y-axis, just above the x-axis.

  2. The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 4 through 4, in increments of 1, are indicated on the x axis. The numbers negative 25 through 100, in increments of 25, are indicated on the y axis. The curve begins to the left of the y axis, high above the x axis. As it moves rightward it goes downward, at first steeply, then more and more slowly as it gets closer and closer to the x axis. Eventually it goes downward toward the x axis so slowly it is almost horizontal. It ends to the right of the y axis, just above the x axis. The curve passes through the point with coordinates negative 3 comma 32, the point with coordinates negative 2 comma 16, and the point with coordinates negative 1 comma 8. It crosses the y-axis a little above the origin and ends to the right of the y-axis, just above the x-axis.

  3. The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 4 through 4, in increments of 1, are indicated on the x axis. The numbers negative 25 through 100, in increments of 25, are indicated on the y axis. The curve begins to the left of the y axis, just above the x axis. As it moves rightward, it goes upward, at first so slowly it is almost horizontal, then more and more quickly. The curve crosses the y-axis a little above the origin, and passes through the point with coordinates 1 comma 8 and the point with coordinates 2 comma 32. It ends to the right of the y-axis, high above the x-axis.

  4. The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 4 through 4, in increments of 1, are indicated on the x axis. The numbers negative 25 through 100, in increments of 25, are indicated on the y axis. The curve begins to the left of the y axis, just above the x axis. As it moves rightward, it goes upward, at first so slowly it is almost horizontal, then more and more quickly. It ends to the right of the y axis, high above the x axis. The curve crosses the y axis a little above the origin, and it passes through the point with coordinates 1 comma 8, the point with coordinates 2 comma 16, and the point with coordinates 3 comma 32. It ends to the right of the y-axis, high above the x-axis.

Toggle Answer

Tip: Press CTRL/Command to toggle answer
Correct Answer: D
Rationale

Choice D is correct. The y-intercept of the graph of an equation is the point with coordinates 0 comma b, where b is the value of y when x equals 0. For the given equation, y equals 4 when x equals 0. It follows that the y-intercept of the graph of the given equation is the point with coordinates 0 comma 4. Additionally, for the given equation, the value of y doubles for each increase of 1 in the value of x. Therefore, the graph contains the points with coordinates 1 comma 8, 2 comma 16, 3 comma 32, and 4 comma 64. Only the graph shown in choice D passes through these points.

Choices A and B are incorrect because these are graphs of decreasing, not increasing, exponential functions. Choice C is incorrect because the value of y increases by a growth factor greater than 2 for each increase of 1 in the value of x.

Question Difficulty: Medium
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
28 / 65 Next