how to graph f(x)=7|x -4|-1

Answer:

here I drew it digitally Hope it helps

Step-by-step explanation:

The graph of the function is a V-shaped curve.

Given that we need to determine the graph of the function f(x) = 7|x - 4| - 1.

To graph the function f(x) = 7|x - 4| - 1, you can follow these steps:

Start by identifying the key points of the function. In this case, the function involves an absolute value, which means it may change direction at the point inside the absolute value.

Set the expression inside the absolute value equal to zero and solve for x to find this critical point:

|x - 4| = 0

x - 4 = 0

x = 4

So, the critical point is x = 4.

Next, consider the behavior of the function on each side of the critical point.

Choose some values of x less than and greater than 4 and substitute them into the function to determine the corresponding y-values.

Let's choose x = 2:

f(2) = 7|2 - 4| - 1

f(2) = 7|-2| - 1

f(2) = 7(2) - 1

f(2) = 14 - 1

f(2) = 13

Let's choose x = 6:

f(6) = 7|6 - 4| - 1

f(6) = 7|2| - 1

f(6) = 7(2) - 1

f(6) = 14 - 1

f(6) = 13

Therefore, we have the points (2, 13) and (6, 13) on the graph.

Plot the critical point and the points you found on the coordinate plane. Mark them on the x-axis and y-axis.

To graph the absolute value part of the function, draw a V-shaped curve with the vertex at the critical point (4, 0).

The arms of the V-shaped curve will pass through the plotted points (2, 13) and (6, 13).

Extend the arms of the V-shaped curve indefinitely in both directions.

Finally, add the constant term (-1) by shifting the entire graph down by 1 unit. This means that every y-value on the graph should be reduced by 1 unit.

Your completed graph of the function f(x) = 7|x - 4| - 1 should resemble a V-shaped curve with its vertex at (4, -1), passing through the points (2, 12) and (6, 12), and extending infinitely in both directions.

The graph of the function is attached.

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