MATH 1050-006
Practice exam 2
1.
6 points Decide whether the following statements are true or false.
100
(a)
L5=500
(b)
=y
(x+y)
+
.
4
x
(e)
(2)2X
(d)
(e)
3 + 6x
9x
2
(f)
2 + x + 1 has 2 different roots.
x
—
x + 1 has 5 different roots.
2. 4 points Caleulate.(Write the answer as a single real number)
41000
(a)
4999
(b)Z
3. 4 points Solve for x where
—8=rO.
5
(a) (x+2)
(b) iEfl-3=O.
4. 4 points Find the implied domains of the following expressions:
(a)
(b)
5.
3 + 2x
x
/2x
—
—
1
1
2 points If f(x) is an invertible function, and f(7)
=
6. 4 points Find the inverse of the following fnnctions.
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10. What is f_1(10)?
(a) f(x)=(x-1)
(b) g(x)
/2x
—
1+5
7. 6 points Divide.
(a)
(b)
4
6x
—
8.
—
5x + 9
+2
2
3x
—
2
x
—
—
(c)
3 + 16x
9x
2
9
2
2x + x + 1
2
x—2
4 points Complete the squares (into the form a(x + c)
2 + d):
(a) —2x
+6x+1
2
(b) 8x
+16x+8
2
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9.
10.
2 points What’s the slope of the line passing through (—1,3) and (6,7)?
6 points Completely factor the following polynonuals.(Your answers should consist of a product of a
real number. monic linear polynomial(s), and monic quadratic polynomial(s) without root)
(a) 3x + 7
(b)
12_41+4
(c) x
—
312
+ 3x
—
2(hint: factors of degree 0 coefficients are possible roots)
11. 1 points How many roots do the following polynomials have?
12.
(a)
2
(b)
12
+ 2x
—
10
+r+5
I points
Find the roots of the polynomial
x2
+ 3x
—
1.
13. 4 points List all the monic linear factors that you know from the graph below.
a
14. 37 points Graph the following functions as precisely and clearly as possible, and write down required
numbers/coordinates (Might include x-,y-intcrccpt, and/or the vertex. See answer sheet for details.):
(a) f: [-1, cc)
[0, cc), f(x) =
5
(b) f:lR—*IR,f(x)=x
(c) f:R—*IR,f(x)=---x+4
(d) 2
f:IR—>IR,f(x)=—x
+
4x+4
:R-{-2}
—*R.f(x) =
(e) f
(f) g : H
R.g(x)
= (I
—
x(r + i)(x + 3)
2
i)
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Scratch paper
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