Mathematics

1.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

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

2.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) = -2x
4 + 4x
3

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

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

f(x) = 2(x – 3)
2 + 1

 A. (3, 1) B. (7, 2) C. (6, 5) D. (2, 1)

4.Find the domain of the following rational function.

f(x) = x + 7/x
2 + 49

 A. All real numbers < 69 B. All real numbers > 210 C. All real numbers ≤ 77 D. All real numbers

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