Pre Calculus Problems and Solutions (Part -1)

Problem 1 :

The point P(3, 8) is on the graph of y = b^x, where b > 1.  The corresponding point P’ on the graph of y + 3 = b^{x + 1} is

A)  (2, 11)

B)  (2, 5)

C)  (4, 11)

D)  (4, 5)

Solution :

Problem 2 :

The function y = f(x) has a domain of {x| 2 ≤ x ≤ 6, x ∈ R} and a range of
{y| -4 ≤ y ≤ 8, y ∈ R}, The function undergoes the transformation y = -f(½x).

The domain and range of the transformed function are shown in row :

Solution :

Problem 3 :

The graph of y = f(x) is transformed into the graph of y = g(x), shown below.

An equation for g(x) in terms of f(x) is

A)  g(x) = f(2x) + 10

B)  g(x) = f(½x) + 10

C)  g(x) = 2f(2x)

D)  g(x) = 2f(½x)

Solution :

Problem 4 :

If Point A(–3, 4) is a point on the graph of y = f(x), then find the corresponding image point, A’, on the graph of

An equation for g(x) in terms of f (x) is

A)  (3, 1)

B)  (3, 7)

C)  (-5, 1)

D)  (-5, 1)

Solution :

Problem 5 :

The loudness of a sound is related to the logarithm of the ratio of the measured intensity, I, to a reference intensity, I₀. The loudness, L, of a sound is measured in decibels, dB, and can be determined using the following formula.

During an international soccer tournament in 2010, a noisemaker called the vuvuzela had a measured loudness of 127 dB at full volume.

If the intensity of the sound of the vuvuzela is 5 000 times greater than the intensity of the sound of a lawn mower, then the measured loudness of the lawn mower, to the nearest decibel, is

A)  3 dB

B)  37 dB

C)  90 dB

D)  123 dB

Solution :

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