1001 Algebra Problems.PDF

Set 48 (Answers begin on page 243)

This problem set focuses on the basic computations
and graphs involving exponentials, as well as applica-
tion of the exponent rules.

753.Ifex= 2 and ey= 3, then e^3 x – 2y=
a.^98 
b.^89 
c. 1
d.–1

754.Simplify: 2x 2 x+1
a. 2 x^2 +x
b. 22 x+ 1
c. 22 –

x2

x

d.^22

• x

x2



755.Simplify: (4x – 1)^2  16
a. 42 x+ 2
b. 4 x
c. 42 x
d. 4 –2x

756.Simplify:

a. 5 x–3

b. 53 x

c. 5 x+ 3

d. 5 –3x

757.Simplify: (ex+ e–x)^2

a.e^2 x+ e–2x

b.e^2 x+ e–2x + 2

c.ex^2 + e–x^2

d.ex^2 + e–x^2 + 2

758.Simplify:

a. 58 x– 1

b. 1253 x– 2

c. 254 x– 1

d. 6252 x– 1

759.Simplify:ex(ex– 1) – e–x(ex– 1)

a.e^2 x– ex– 1 + e–x

b.e^2 x+ ex– 1 + e–x

c.e^2 x+ 2ex– 1

d.e^2 x+ 1 – 2e–x

760.Simplify:

a.e^2 x+ 1

b.e^4 x+ 1

c.e–4x+ 1

d.e–2x+ 1

761.Which of the following statements is true?

a.Ifb  1, the graph ofy= bxgets very close to

the x-axis as the x-values move to the right.

b.Ifb  1, the graph ofy= bxgets very close to

the x-axis as the x-values move to the left.

c.Ifb  1, the graph ofy= bxgrows without

bound as the x-values move to the left.

d.Ifb  1, the y-values associated with the

graph of y = bxgrow very rapidly as the x-

values move to the right.

ex(ex– e–x) + e–x(ex+ e–x)

e–^2 x

(5^3 x– 1)^3 ^5 x – 1

52 x

54 x ^12

 52 x– 6

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