Model Exam

Which of the following is the general form of an exponential function?

• y=a+bx

• y=ax^2+bx+c

• y=b^x

• y=log(x)

Answer explanation

The general form of an exponential function is y=b^x, where b is the base and x is the exponent. This choice represents the correct form of an exponential function.

Which of the following statements is true about the graph of y=e^x

• It passes through the point (0, 0).

• It is always decreasing.

• It has a horizontal asymptote at y=0

• It crosses the x-axis.

Answer explanation

The graph of y=e^x has a horizontal asymptote at y=0, which means it approaches but never reaches y=0 as x approaches negative or positive infinity.

Which equation represents the logarithmic form of the exponential equation 10^y=25?

• log(25)=y

• log(y)=25

• y=25log10

Answer explanation

The correct choice is log(25)=y because in logarithmic form, the base (10) is the subscript, the result (25) is the number, and the exponent (y) is the answer.

Which of the following best describes a hole in the graph of a rational function?

• A point where the function is undefined and the denominator is zero

• A point where the function crosses the x-axis

• A point where the function has a vertical asymptote

• A point where the function's numerator equals zero

Answer explanation

A hole in the graph of a rational function occurs at a point where the function is undefined and the denominator is zero.

Which of the following best describes a hole in the graph of a rational function?

• A point where the function has a vertical asymptote

• A point where the numerator and denominator both equal zero and cancel out

• A point where the function crosses the x-axis

• A point where the function is undefined and goes to infinity

Answer explanation

A point where the numerator and denominator both equal zero and cancel out

Find cotΘ.

• 3/4

• 4/3

• 5/4

• 5/3

Answer explanation

To find cotΘ, use the formula cotΘ = 1/tanΘ. Since tanΘ = 3/4, cotΘ = 1/(3/4) = 4/3. Therefore, the correct answer is 4/3.

The amount of ibuprofen (medicine for headaches) breaks down by 30% each hour. If a person took a 200 milligram ibuprofen, how much will be left after 3 hours?

• 5.4 mg

• 68.6 mg

• .0054 mg

• 2,400,000 mg

Answer explanation

After 3 hours, 68.6 mg of ibuprofen will be left. This is calculated by taking 200 mg and multiplying by (1 - 0.30) three times.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
Is the population of elephants increasing or decreasing?

• Increasing

• Decreasing

Answer explanation

The population of elephants is increasing because the expression 12(1.015)^t represents exponential growth, where the population grows over time.

The period of a function is

• the length of one cycle

• how high and low the function goes from the center line

• the range of the function

Answer explanation

The period of a function is the length of one cycle, indicating how often the function repeats itself.

what is the amplitude of the graph shown

• 1

• 2

• 3

• 4

Answer explanation

The correct amplitude of the graph shown is 2, which corresponds to the distance from the midline to the peak of the wave.