How do you graph #y = -7|x-3| - 4 #?

Answer 1

Reflect the graph over the y-axis, translate the graph 3 units to the right and 4 units down, and apply a scale factor of 7.

The vertex of the graph will be #(3,-4)#. The graph will also be facing down. As for the scale factor, for every 1 unit to the left or right of the vertex, 7 "units" will be covered downwards.

graph{y=-7abs(x-3)-4 [-6.955, 13.045, -12.88, -2.88]}

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Answer 2

To graph the function ( y = -7|x-3| - 4 ), follow these steps:

  1. Identify the vertex of the absolute value function, which is at the point (3, -4).

  2. Plot the vertex on the coordinate plane.

  3. Determine the direction of the graph. Since the coefficient of the absolute value term is negative (-7), the graph will open downwards.

  4. Choose points on either side of the vertex to determine additional points for the graph. For example, if x = 0, then ( y = -7|0-3| - 4 = -7(3) - 4 = -21 - 4 = -25 ). So, the point (0, -25) is on the graph.

  5. Draw the graph by connecting the points. The graph will be a downward-opening "V" shape, centered at the vertex (3, -4).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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