Semester Test 2nd block

Front

What is the product of the matrices \( \begin{pmatrix} 1 & 2 \\ 6 & -8 \end{pmatrix} \) and \( \begin{pmatrix} -3 & -5 \\ -5 & -11 \end{pmatrix} \)?

Back

The product is \( \begin{pmatrix} -3 & -5 \\ -5 & -11 \end{pmatrix} \).

Front

What is the logarithmic identity for \( \log(4x) \)?

Back

The identity is \( \log(4) + \log(x) \).

Front

What does it mean if a function exhibits exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value.

Front

What is the domain of the function \( f(x) = \sqrt{x + 4} \)?

Back

The domain is \( [-2, \infty) \).

Front

Describe the transformations of the function \( g(x) = \sqrt{x + 4} - 6 \) from its parent function.

Back

The function shifts left 4 units and down 6 units.

Front

What is the definition of a matrix product?

Back

The matrix product is the result of multiplying two matrices, calculated by taking the dot product of rows and columns.

Front

What is the logarithmic property that allows you to combine logs?

Back

The property states that \( \log(a) + \log(b) = \log(ab) \).

Front

How do you identify exponential growth?

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value.

Front

What is the range of the function \( f(x) = \sqrt{x + 4} \)?

Back

The range is \( [0, \infty) \).

Front

What is the transformation of a function when it is shifted to the right?

Back

A right shift occurs when you replace \( x \) with \( x - c \) in the function, where \( c \) is a positive constant.