I need help, and I can't find the answer. Can you explain how to do this please? I don't want the answer only, I need to know the answer, and how to find it. Thank you!!
9. What is the equation of the absolute value function? (1 point)
y = 6|x + 2| –2
y = 6|–x – 2| + 2
y = –6|x + 2| – 2
y = –6|x – 2| – 2
those are all equation using the absolute value function.
They are all v-shaped, opening up or down. To see what they look like, go to
wolframalpha.com
and type in the box
plot 6|x + 2| –2
or the other formulas, and see what the graphs look like. It's a good place to play around with variations on a theme.
Certainly! I'd be happy to explain how to find the equation of the absolute value function.
The equation of an absolute value function can be determined based on the general form:
y = a|x - h| + k
In this form, "a" represents the vertical stretch or compression, "h" represents the horizontal shift, and "k" represents the vertical shift of the graph of the function.
To find the equation of the absolute value function, we need to determine the values of "a," "h," and "k" based on the given options.
Let's go through each option:
Option 1: y = 6 |x + 2| - 2
In this equation, "a" is positive 6, indicating a vertical stretch by a factor of 6. "h" is -2, representing a horizontal shift of 2 units to the left. "k" is -2, leading to a vertical shift of 2 units downward.
Option 2: y = 6 |-x - 2| + 2
Similar to the previous option, "a" is positive 6, resulting in a vertical stretch by a factor of 6. "h" remains -2, indicating a horizontal shift of 2 units to the right. "k" is positive 2, leading to a vertical shift of 2 units upward.
Option 3: y = -6 |x + 2| - 2
In this equation, "a" is negative 6, representing a vertical reflection and stretch by a factor of 6. "h" remains -2, indicating a horizontal shift of 2 units to the left. "k" is -2, resulting in a vertical shift of 2 units downward.
Option 4: y = -6 |x - 2| - 2
Similar to the previous option, "a" is negative 6, leading to a vertical reflection and stretch by a factor of 6. "h" remains 2, indicating a horizontal shift of 2 units to the right. "k" is -2, resulting in a vertical shift of 2 units downward.
Therefore, the correct equation of the absolute value function is Option 4:
y = -6 |x - 2| - 2
To find the correct answer and understand how to solve it, we analyzed each option's parameters and their impact on the absolute value function's equation.