Question

Which absolute value equation creates the lower function and The graft be sure to consider the scale of x and y axis when evaluating the question

Answer 1

To create a function that has a lower graph when dealing with absolute value equations, you typically deal with equations that take the form:

\[ y = a |x - h| + k \]

where:
- \( a \) determines the vertical stretch or compression (and direction if negative),
- \( h \) is the horizontal shift,
- \( k \) is the vertical shift.

If you want the graph to be "lower," you might want to ensure that \( k \) is a negative value or relatively low, as this shifts the graph downward.

For example, an equation like:

\[ y = |x| - 2 \]

This will create a V-shaped graph that opens upwards and is shifted downwards by 2 units, making it lower than the standard absolute value graph \( y = |x| \).

If you were considering other transformations or shifts, here are a few more examples of absolute value equations that might create "lower" graphs:

1. **Down shift**:
\[ y = |x| - 3 \]
Shifts the standard graph down by 3 units.

2. **Inversion**:
\[ y = -|x| + 1 \]
This creates an upside-down V-shape that starts at \( (0, 1) \) and goes downward.

3. **Combined transformations**:
\[ y = -2 |x| - 4 \]
This graph will have a steeper slope because of the -2, and it is shifted down by 4 units.

By evaluating the specific equation and plotting it based on these transformations, you can visualize how the graph behaves with respect to the x and y axes. Ultimately, the choice of how "lower" you want the function to be will dictate how much you shift it downwards or adjust the scale of the graph.