2024 Fall Final Exam Review III.

Front

What happens to the equation of a linear function when it is shifted down by 5 units?

Back

The y-intercept decreases by 5.

Front

How does changing the slope of a linear function to be twice as steep affect its equation?

Back

The slope coefficient is multiplied by 2.

Front

What is the general form of an exponential function?

Back

y = a(b^x), where a is a constant and b is the base.

Front

If f(x) = x, what is the equation of g(x) if g(x) is f(x) shifted up by 6 units?

Back

g(x) = x + 6.

Front

What does it mean for a function to exhibit exponential behavior?

Back

The function grows or decays at a rate proportional to its current value.

Front

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

Back

Look for a constant ratio between consecutive y-values as x increases.

Front

What is the effect of adding a constant to a function's output?

Back

It shifts the graph vertically.

Front

What is the effect of multiplying a function by a constant less than 1?

Back

It compresses the graph vertically.

Front

What does the graph of g(x) = 1/4 f(x) represent in relation to f(x)?

Back

It represents a vertical compression of f(x) by a factor of 1/4.

Front

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

Back

It determines the growth or decay rate of the function.