2 errors in step 3 -15 + 7 = -8 not +22
also a negative devided by a postive is a negative (the x on the last step)
Step-by-step explanation:
I would like to get through High School, become a writer, and help people out with their homework. For my first goal I will do my work, for my second goal I will start publishing my books online first then when I'm more known I will write publicly. For my third goal I will help my friends do their homework- and others who need help- with their homework and get to college. It may take some time but I will get it done.
Explanation:
I would like to get through High School, become a writer, and help people out with their homework. For my first goal I will do my work, for my second goal I will start publishing my books online first then when I'm more known I will write publicly. For my third goal I will help my friends do their homework- and others who need help- with their homework and get to college. It may take some time but I will get it done.
Explanation:
f(x) = -2|x-2| +4
Step-by-step explanation:
Step 1: recognize this as an inverted, scaled, and translated absolute value function.
Step 2: identify the scale factor as 2, because each section has a "rise" of 2 for each "run" of 1. The scale factor is -2 because the function is inverted (reflected across the x-axis).
Step 3: identify the vertex* as (2, 4).
Step 4: Use the scale factor and translation information to make the transformation ... (let abs(x) represent the absolute value function)
f(x) = (scale factor)×abs(x -horizontal shift) + (vertical shift)
f(x) = -2|x -2| +4
_____
* The vertex is an identifiable point on the graph of this function. Knowing how the vertex is translated tells you how the whole function is translated. In general, you want to use an identifiable point (a turning point, point of symmetry, extreme point, whatever) when you're trying to determine the translation. For some functions, like a line, there is no specific identifiable point, so determining any specific translation is difficult or impossible.
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Comment on writing functions from graphs
One of the reasons for studying different functions is so you can learn to recognize their shape, and associate a formula and certain properties with that shape.
_____
The attached graph shows the parent absolute value function in blue and the transformed function f(x) in red.
f(x) = -2|x-2| +4
Step-by-step explanation:
Step 1: recognize this as an inverted, scaled, and translated absolute value function.
Step 2: identify the scale factor as 2, because each section has a "rise" of 2 for each "run" of 1. The scale factor is -2 because the function is inverted (reflected across the x-axis).
Step 3: identify the vertex* as (2, 4).
Step 4: Use the scale factor and translation information to make the transformation ... (let abs(x) represent the absolute value function)
f(x) = (scale factor)×abs(x -horizontal shift) + (vertical shift)
f(x) = -2|x -2| +4
_____
* The vertex is an identifiable point on the graph of this function. Knowing how the vertex is translated tells you how the whole function is translated. In general, you want to use an identifiable point (a turning point, point of symmetry, extreme point, whatever) when you're trying to determine the translation. For some functions, like a line, there is no specific identifiable point, so determining any specific translation is difficult or impossible.
_____
Comment on writing functions from graphs
One of the reasons for studying different functions is so you can learn to recognize their shape, and associate a formula and certain properties with that shape.
_____
The attached graph shows the parent absolute value function in blue and the transformed function f(x) in red.
It will provide an instant answer!