What is the relationship between the graphs of $$f(x) = \log_2 x$$ , $$g(x) = \log_2(2x)$$ , and $$h(x) = \log_2(\frac{x}{2})$$ ?

The graph of $$f$$ is shifted one unit up to create the graph of $$g$$ , and shifted one unit down to create the graph of $$h$$ . All three graphs have the same domain but different x-intercepts.

How do you find the number of bacteria after a certain time using the function $$B(t) = 100e^{0.1066t}$$ ?

Substitute the value of $$t$$ into the function to calculate $$B(t)$$ .

How do you determine the domain of the function $$f(x) = \log_2 x$$ ?

The domain is all positive real numbers, i.e., $$x > 0$$ .

What transformation occurs when the graph of $$f(x) = 4^x$$ is shifted left by 3 units?

The new function is $$f(x) = 4^{(x + 3)}$$ .

How do you solve for time when given an exponential growth function and a target population?

Set the function equal to the target population and solve for $$t$$ .

What is the significance of the constant in the exponential function $$B(t) = 100e^{0.1066t}$$ ?

The constant $$100$$ represents the initial number of bacteria present at time $$t = 0$$ .

What is the effect of changing the base of a logarithm on its graph?

Changing the base alters the steepness and position of the graph but does not change the x-intercept.

How do you convert an exponential equation to logarithmic form?

If $$a^b = c$$ , then it can be expressed as $$\log_a(c) = b$$ .

What is the formula for calculating the x-intercept of the function $$g(x) = \log_2(2x)$$ ?

Set $$g(x) = 0$$ and solve for $$x$$ .

What is the relationship between the growth rate and the steepness of an exponential function?

A higher growth rate results in a steeper curve in the graph of the exponential function.

How do you round a number to the nearest whole number?

Look at the digit to the right of the last digit you want to keep; if it's 5 or more, round up.

CAT Pre-Test Unit 3 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

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2.

FLASHCARD QUESTION

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3.

FLASHCARD QUESTION

Front

What is the general form of an exponential growth function?

Back

4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

Front

What does the base of a logarithm represent in the context of exponential functions?

Back

The base of a logarithm indicates the factor by which the quantity grows or shrinks in an exponential function.

6.

FLASHCARD QUESTION

Front

What is the x-intercept of a logarithmic function?

Back

The x-intercept is the point where the graph crosses the x-axis, which occurs when the output of the function is zero.

7.

FLASHCARD QUESTION

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Back

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