PRE-CAL MATH TEST SOLUTIONS

A/

1)Test the following to see if they are functions. If they are

 i) state one-to-one or many-to-one ii) state the domain.

If they're not, say why.

 a) x = y 2 not a functionsince b) y = x2 - 3x - 28a function, many-to-onedomain is R c) y =a 1-1 functiondomain R but x ! 10 d) f(x) =not a functionsame reason as a) e) y = x is a 1 to 1 functiondomain R.

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2) Write the equation of the line:

a) through (-2, 3) parallel to y = -5x + 7
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b) through (-2, 3) and ( 1, 5)
slope = 2 / 3 so
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c) through the mid-point of A (-6, 3) B (4, 7) perpendicular to 3x - 5y + 10 = 0
slope of 3x - 5y + 10 = 0 is 3 / 5, so perpendicular slope = -5 / 3
midpoint is (-1, 5)
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d) through (-6, 3) parallel to the Y-axis
x = - 6
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e) that bisects A (1, -3) B (7, - 7) at right angles.
midpoint is (4, - 5); slope is - 4 / 6 = - 2/3 so perpendicular slope = 3 / 2
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3) State the slope, y-intercept and x-intercept of 2x + 3y =24

slope = -A / B = -2 / 3
y-intercept : set x = 0 so b = 8
x-intercept : set y = 0 so a = 12

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B/ 1) f(x) = 2x2 - 60x + 25

a) h = -b / 2a = 60 / 4 = 15, k = f(h) = - 425
f(x) = 2(x - 15) 2 - 425
b) the graph is a parabola
i) it opens upwards
ii) the vertex is ( 15, - 425 )
iii) the equation of the axis of symmetry is x = 15
iv) domain is R, range is [- 425, º ] , extreme value is - 425
c) draw the graph.

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2) Find the x-intercepts or ZEROS (if any) for:

 a) y = x2 - 5x x(x - 5) = 0 x = 0 or x = 5 b) y = x2 - 4x - 21 (x - 7)(x + 3) = 0x = 7 or x = - 3 c) y = x2 - 4x + 5it doesn't factor, use quadratic formula b 2 - 4ac = -4 < 0, no roots, min k = 1

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3) A farmer has 60 meters of fencing to enclose a rectagular field along a riverbank.
The side along the river needs no fence since his cows can't swim.

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