Review Units 7, 8, 9 & 10

Front

What is a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, in the expression \(\log_b(a) = c\), it means that \(b^c = a\).

Front

What is the correlation coefficient (r)?

Back

The correlation coefficient (r) is a statistical measure that describes the strength and direction of a relationship between two variables. It ranges from -1 to 1.

Front

How does the degree of a polynomial affect its end behavior?

Back

The end behavior of a polynomial function is determined by its degree and the sign of its leading coefficient. If the degree is even, both ends of the graph will go in the same direction; if odd, they will go in opposite directions.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It influences the end behavior of the polynomial.

Front

Evaluate \(\log_3(9)\).

Back

The answer is 2, because \(3^2 = 9\).

Front

Evaluate \(\log_5(125)\).

Back

The answer is 3, because \(5^3 = 125\).

Front

What is the product of \((-7x^2)(4x^4)\)?

Back

The product is \(-28x^6\).

Front

What does a correlation coefficient of \(r = -0.95\) indicate?

Back

It indicates a strong negative linear relationship between the two variables.

Front

What does a correlation coefficient of \(r = 0\) indicate?

Back

It indicates no linear relationship between the two variables.

Front

What does a correlation coefficient of \(r = 1\) indicate?

Back

It indicates a perfect positive linear relationship between the two variables.