SQB Logo
sqbofficial

Question which-

2.1 Nonlinear Functions - Quadratic graphs and vertex form
0:00

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?

A.

 

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 indied on the x axis. The numbers negative 25 through 100, in increments of 25, are indied 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.

 

B.

 

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 indied on the x axis. The numbers negative 25 through 100, in increments of 25, are indied 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.

 

C.

 

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 indied on the x axis. The numbers negative 25 through 100, in increments of 25, are indied 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.

 

D.

 

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 indied on the x axis. The numbers negative 25 through 100, in increments of 25, are indied 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.

 

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

Hard-difficulty · SAT Math · Nonlinear Functions — Quadratic graphs and vertex form. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

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.

 

More Nonlinear Functions practice questions

Browse all Passport to Advanced Math practice questions or return to the full SAT question bank.