Take the function for example. The graph for is

If we were to change the function to , our phase shift is . This means we need to shift our entire graph units to the left.

Our new graph is the following

Take the function for example. The graph for is

If we were to change the function to , our phase shift is . This means we need to shift our entire graph units to the left.

Our new graph is the following

The amplitude of a sinusoidal function is unless amplified by a constant in front of the equation. In this case, the amplitude is , so the front constant is .

The graph moves through the origin, so it is either a sine or a shifted cosine graph.

It repeats once in every , as opposed to the usual , so the period is doubled, the constant next to the variable is .

The only answer in which both the correct amplitude and period is found is:

The amplitude of a sinusoidal function is unless amplified by a constant in front of the equation. In this case, the amplitude is , so the front constant is .

The graph moves through the origin, so it is either a sine or a shifted cosine graph.

It repeats once in every , as opposed to the usual , so the period is doubled, the constant next to the variable is .

The only answer in which both the correct amplitude and period is found is:

The general form for the secant transformation equation is . represents the phase shift of the function. When considering we see that . So our phase shift is and we would shift this function units to the left of the original secant function’s graph.

The general form for the secant transformation equation is . represents the phase shift of the function. When considering we see that . So our phase shift is and we would shift this function units to the left of the original secant function’s graph.

The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine. Similarly, the coefficient associated with the x-value is related to the function's period. The largest coefficient associated with the sine in the provided functions is 2; therefore the correct answer is .

The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.

The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine. Similarly, the coefficient associated with the x-value is related to the function's period. The largest coefficient associated with the sine in the provided functions is 2; therefore the correct answer is .

The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.

Looking at our graph, we can tell that the period is . Using the formula

where is the coefficient of and is the period, we can calculate

This eliminates one answer choice. We then retrun to our graph and see that the amplitude is 3. Remembering that the amplitude is the number in front of the function, we can eliminate two more choices.

We then examine our graph and realize it contains the point . Plugging 0 into our two remaining choices, we can determine which one gives us 4 for a result.

Looking at our graph, we can tell that the period is . Using the formula

where is the coefficient of and is the period, we can calculate

This eliminates one answer choice. We then retrun to our graph and see that the amplitude is 3. Remembering that the amplitude is the number in front of the function, we can eliminate two more choices.

We then examine our graph and realize it contains the point . Plugging 0 into our two remaining choices, we can determine which one gives us 4 for a result.