Unit 6 Post - Assessment - Algebra: Concepts and Connections

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What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent. It represents growth or decay processes.

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How do you translate a function vertically?

Back

To translate a function vertically, you add or subtract a constant from the function. For example, f(x) + k translates the graph up by k units, while f(x) - k translates it down by k units.

Front

What is the average rate of change of a function?

Back

The average rate of change of a function f over an interval [a, b] is given by the formula (f(b) - f(a)) / (b - a). It represents the slope of the secant line connecting the points (a, f(a)) and (b, f(b)).

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What does it mean for a function to be reflected across the x-axis?

Back

A function is reflected across the x-axis when all y-values are multiplied by -1. For example, if f(x) is the original function, the reflected function is g(x) = -f(x).

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have the form f(x) = mx + b, where m is the slope and b is the y-intercept. Quadratic functions have the form f(x) = ax^2 + bx + c, where a, b, and c are constants, and the graph is a parabola.

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1. For example, if f(x) is stretched by a factor of k, the new function is g(x) = k * f(x).

Front

What is a vertical shrink of a function?

Back

A vertical shrink occurs when the output values of a function are multiplied by a factor between 0 and 1. For example, if f(x) is shrunk by a factor of k, the new function is g(x) = k * f(x).

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How do you identify an exponential function from a table of values?

Back

An exponential function will show a constant multiplicative rate of change between consecutive y-values. If each y-value is multiplied by the same factor to get the next y-value, it is exponential.

Front

What is the significance of the base in an exponential function?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What does it mean for a function to be translated horizontally?

Back

To translate a function horizontally, you add or subtract a constant from the input variable. For example, f(x - k) translates the graph to the right by k units, while f(x + k) translates it to the left by k units.