Describe how the graphs of y=|x| and y=|x+3| are related.
-The two graphs have the same shape but the second graph is shifted 3 units up
-the two graphs have the same shape but the second graph is shifted 3 units down
-the two graphs have the same shape but the second graph is shifted 3 units left
-the two graphs have the same shape but the second graph is shifted 3 units right
sorry if this is a pathetic question, I'm pretty bad at math
Generally speaking:
if you have y = f(x)
then something like y = f(x+5) would be a horizontal shift of 5 units to the left
and something like y = f(x-5) would be a horizontal shift of 5 units to the right
so yours would be 3 units to the left
Proof: (copy and paste this URL)
www.wolframalpha.com/input/?i=y%3D%7Cx%7C+%2C+y%3D%7Cx%2B3%7C
Not a problem at all! Understanding the relationship between graphs can sometimes be challenging. To compare the graphs of y=|x| and y=|x+3|, let's break it down step by step.
The equation y=|x| represents the absolute value function. It takes the input value (x) and returns the positive value of x. This means that for any positive x, the function remains the same, but for any negative x, the function negates the negative sign and returns the positive value.
On the other hand, the equation y=|x+3| applies a shift to the x-values in addition to taking their absolute value. This means that before finding the absolute value, the x-values are increased by 3. For instance, if the original x-value was 1, it would now be (1+3)=4. This shifting affects both the positive and negative values of x.
Now, let's consider the options you provided:
- The two graphs have the same shape, but the second graph is shifted 3 units up: This statement is not accurate because the shift of the graph y=|x+3| is not upward but rather horizontally.
- The two graphs have the same shape, but the second graph is shifted 3 units down: This statement is also not accurate as the shift is not downward but horizontally.
- The two graphs have the same shape, but the second graph is shifted 3 units left: This statement is not correct since the shift is not leftwards but horizontally.
- The two graphs have the same shape, but the second graph is shifted 3 units right: This statement is accurate! By adding 3 to the x-values, the graph y=|x+3| is shifted three units to the left compared to y=|x|.
So, the correct answer is: "The two graphs have the same shape, but the second graph is shifted 3 units right."