Honors Precalculus - Chapter 3 Review

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

Determine the horizontal asymptote for the function f(x) = 3(2)^(x-4) + 5.

Back

y = 5

Front

How do you solve the equation 19^(x-2) - 6 = 64?

Back

First, isolate the exponential term: 19^(x-2) = 70. Then take the logarithm of both sides and solve for x.

Front

What is the solution to the equation 19^(x-2) - 6 = 64 rounded to the nearest ten-thousandth?

Back

x = 3.4429

Front

What is the natural logarithm function?

Back

The natural logarithm function, denoted as ln(x), is the logarithm to the base e, where e is approximately 2.71828.

Front

Solve the equation 5 ln(3x - 2) = 15.

Back

x = 7.36

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

Find the domain of the function f(x) = 1/(x-1).

Back

The domain is (-∞, 1) ∪ (1, ∞) because x cannot equal 1.

Front

What does it mean to condense logarithmic expressions?

Back

Condensing logarithmic expressions involves combining multiple logarithms into a single logarithm using properties of logarithms.

Front

Condense the expression 5 log(a) - 25 log(b).

Back

log( (a^5)/(b^25) )