Gateway Quiz Section11EvaluationGraphingTest

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Problem 1.

(1 point)

What is the area of the blue rectangle? The graphed function is $y=2x(x-1)$ .
area =

graph of an upward opening parabola in the first quadrant, having x-intercepts at zero and a positive x-value between x=0 and x=2. the blue rectangle has a base lying along the x-axis between x=2 and x=4, and upper-left corner on the parabola.

Problem 2.

(1 point)

What are the coordinates of the point $Q$ in the following graph of $y = \ln(x)$ ?
$x,y =$
(Enter the parts of your answer in order, separated by a comma.)

graph of a curve with vertical asymptote at the negative y-axis with positive slope and negative concavity. the x-intercept is P, and at x=e the point on the curve (which has y>0) is labeled Q.

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Problem 3.

(1 point)

What are the coordinates of the point $Q$ in the following graph of $y = 5e^{-0.2x}$ ?
$x,y =$
(Enter the parts of your answer in order, separated by a comma.)

graph of a curve in the first quadrant that is concave up and has negative slope. it has y-intercept P and at x=10 is at a point Q that has positive y-coordinate.

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Problem 4.

(1 point)

What are the coordinates of the point $P$ in the following graph of $y + 2x - 3.04 = 0$ ?
$x,y =$
(Enter the parts of your answer in order, separated by a comma.)

graph of a downward sloping line extending across the 1st quadrant, with y-intercept P and x-intercept Q.

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Problem 5.

(1 point)

What is the area of the blue rectangle? The graphed function is $y=(x-1)^2+1$ .
area =

graph of an upward opening parabola with positive y-intercept and minimum. the blue rectangle has a base lying along the x-axis from x=3 to x=3.1 and top-left corner on the parabola.

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Problem 6.

(1 point)

What are the coordinates of the point $R$ shown in the following graph of $y = 2x$ and $y=8-2x$ ?
$x,y =$
(Enter the parts of your answer in order, separated by a comma.)

graph of two lines in the first quadrant, one with negative slope passing through the y-intercept P and x-intercept R, the other with positive slope passing through the origin. the lines intersect at the point Q.

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Problem 7.

(1 point)

What are the coordinates of the point $P$ in the following graph of $y = -x(x-2)$ ?
$x,y =$
(Enter the parts of your answer in order, separated by a comma.)

graph of a downward opening parabola with x-intercepts P at the origin and Q on the positive x-axis.

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Problem 8.

(1 point)

What is the area of the blue rectangle? The graphed function is $y=x^3+2$ .
area =

graph of a function with positive y-intercept, curving upwards through the first quadrant. the blue rectangle has a base lying along the x-axis between x=1 and x=1.5, and upper-left corner on the function.

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Problem 9.

(1 point)

What is the slope of the blue line segment? The black function is $y = x(5 - x)$ .
slope =

graph of the an downward opening parabola with x-intercepts at x=0 and x greater than 3, with a blue line segment joining the points on the parabola with x=1 and x=3.

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Problem 10.

(1 point)

What are the coordinates of the point $Q$ shown in the following graph of $y = 3+x$ and $y=x(x-1)$ ?
$x,y =$
(Enter the parts of your answer in order, separated by a comma.)

graph of a line with positive slope and upward opening parabola. the line has positive y-intercept and intersects the parabola at P, where x is negative, and R, where x is positive. the parabola intersects the x-axis at the origin and at the point Q to the right of the origin.

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