college algebra 24

Question 1 (5 points)

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

f(x) = 2(x – 3)² + 1

Question 1 options:

	(3, 1)
	(7, 2)
	(6, 5)
	(2, 1)

Question 2 (5 points)

Solve the following polynomial inequality.

3x² + 10x – 8 ≤ 0

Question 2 options:

	[6, 1/3]
	[-4, 2/3]
	[-9, 4/5]
	[8, 2/7]

Question 3 (5 points)

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.

g(x) = x + 3/x(x + 4)

Question 3 options:

	Vertical asymptotes: x = 4, x = 0; holes at 3x
	Vertical asymptotes: x = -8, x = 0; holes at x + 4
	Vertical asymptotes: x = -4, x = 0; no holes
	Vertical asymptotes: x = 5, x = 0; holes at x – 3

Question 4 (5 points)

If f is a polynomial function of degree n, then the graph of f has at most __________ turning points.

Question 4 options:

	n – 3
	n – f
	n – 1
	n + f

Question 5 (5 points)

8 times a number subtracted from the squared of that number can be expressed as:

Question 5 options:

	P(x) = x + 7x. $$ P ( x ) = x + 7 x .
	P(x) = x2 − 8x. $$ P ( x ) = x 2 – 8 x .
	P(x) = x − x. $$ P ( x ) = x – x .
	P(x) = x2+ 10x. $$ P ( x ) = x 2 + 10 x .

Question 6 (5 points)

Solve the following polynomial inequality.

9x² – 6x + 1 < 0

Question 6 options:

	(-∞, -3)
	(-1, ∞)
	[2, 4)
	Ø

Question 7 (5 points)

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = -2x⁴ + 4x³

Question 7 options:

	x = 1, x = 0; f(x) touches the x-axis at 1 and 0
	x = -1, x = 3; f(x) crosses the x-axis at -1 and 3
	x = 0, x = 2; f(x) crosses the x-axis at 0 and 2
	x = 4, x = -3; f(x) crosses the x-axis at 4 and -3

Question 8 (5 points)

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x², but with the given point as the vertex (5, 3).

Question 8 options:

	f(x) = (2x – 4) + 4
	f(x) = 2(2x + 8) + 3
	f(x) = 2(x – 5)2 + 3
	f(x) = 2(x + 3)2 + 3

Question 9 (5 points)

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

f(x) = -2(x + 1)² + 5

Question 9 options:

	(-1, 5)
	(2, 10)
	(1, 10)
	(-3, 7)

Question 10 (5 points)

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.

f(x) = x/x + 4

Question 10 options:

	Vertical asymptote: x = -4; no holes
	Vertical asymptote: x = -4; holes at 3x
	Vertical asymptote: x = -4; holes at 2x
	Vertical asymptote: x = -4; holes at 4x

Question 11 (5 points)

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = x³ + 2x² – x – 2

Question 11 options:

	x = 2, x = 2, x = -1; f(x) touches the x-axis at each.
	x = -2, x = 2, x = -5; f(x) crosses the x-axis at each.
	x = -3, x = -4, x = 1; f(x) touches the x-axis at each.
	x = -2, x = 1, x = -1; f(x) crosses the x-axis at each.

Question 12 (5 points)

Based on the synthetic division shown, the equation of the slant asymptote of f(x) = (3x² – 7x + 5)/x – 4 is:

Question 12 options:

	y = 3x + 5.
	y = 6x + 7.
	y = 2x – 5.
	y = 3x2 + 7.

Question 13 (5 points)

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = x²(x – 1)³(x + 2)

Question 13 options:

	x = -1, x = 2, x = 3 ; f(x) crosses the x-axis at 2 and 3; f(x) touches the x-axis at -1
	x = -6, x = 3, x = 2 ; f(x) crosses the x-axis at -6 and 3; f(x) touches the x-axis at 2.
	x = 7, x = 2, x = 0 ; f(x) crosses the x-axis at 7 and 2; f(x) touches the x-axis at 0.
	x = -2, x = 0, x = 1 ; f(x) crosses the x-axis at -2 and 1; f(x) touches the x-axis at 0.

Question 14 (5 points)

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x² or g(x) = -3x², but with the given maximum or minimum.

Minimum = 0 at x = 11

Question 14 options:

	f(x) = 6(x − 9) $$ f ( x ) = 6 ( x – 9 )
	f(x) = 3(x − 11)2 $$ f ( x ) = 3 ( x – 11 )
	f(x) = 4(x + 10) $$ f ( x ) = 4 ( x + 10 )
	f(x) = 3(x2 − 15)2 $$ f ( x ) = 3 ( x 2 – 15 )

Question 15 (5 points)

The graph of f(x) = -x² __________ to the left and __________ to the right.

Question 15 options:

	falls; rises
	rises; rises
	falls; falls
	rises; rises

Question 16 (5 points)

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = x⁴ – 9x²

Question 16 options:

	x = 0, x = 3, x = -3; f(x) crosses the x-axis at -3 and 3; f(x) touches the x-axis at 0.
	x = 1, x = 2, x = 3; f(x) crosses the x-axis at 2 and 3; f(x) crosses the x-axis at 0.
	x = 0, x = -3, x = 5; f(x) touches the x-axis at -3 and 5; f(x) touches the x-axis at 0.
	x = 1, x = 2, x = -4; f(x) crosses the x-axis at 2 and -4; f(x) touches the x-axis at 0.

Question 17 (5 points)

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers.

f(x) = x³ – x – 1; between 1 and 2

Question 17 options:

	f(1) = -1; f(2) = 5
	f(1) = -3; f(2) = 7
	f(1) = -1; f(2) = 3
	f(1) = 2; f(2) = 7

Question 18 (5 points)

40 times a number added to the negative square of that number can be expressed as:

Question 18 options:

	A(x) = x2 + 20x. $$ A ( x ) = x 2 + 20 x .
	A(x) = −x + 30x. $$ A ( x ) = – x + 30 x .
	A(x) = −x2 − 60x. $$ A ( x ) = – x 2 – 60 x .
	A(x) = −x2 + 40x. $$ A ( x ) = – x 2 + 40 x .

Question 19 (5 points)

Find the domain of the following rational function.

f(x) = x + 7/x² + 49

Question 19 options:

	All real numbers < 69
	All real numbers > 210
	All real numbers ≤ 77
	All real numbers

Question 20 (5 points)

The perimeter of a rectangle is 80 feet. If the length of the rectangle is represented by x, its width can be expressed as:

Question 20 options:

	80 + x.
	20 – x.
	40 + 4x.
	40 – x.

 

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