Pretend the parentheses are absolute value bars.
What is the graph of y = (x) and its translation to the graph of y = (x + 3)+1?
I know I can't post the graph picture here, but I'm confuzzled on how to solve the problem. Please explain how! Thank you so much! <3
take it in two steps
y = │x+3│ moved y = │x│ to the left 3 units
then y = │x+3│ + 1 would move the last graph up 1 unit.
so y = │x│ , was moved 3 units to the left and 1 unit up.
I like "confuzzled"
Thank you! :D
To understand the graph of y = |x|, let's break down the steps:
1. Start with the basic graph of y = x. This is a straight line passing through the origin, with a slope of 1.
2. To consider the absolute value |x|, we need to ensure that the graph is non-negative, as the absolute value of a number is its positive value. So, we reflect the negative portion of the graph (below the x-axis) to make it positive.
Now, let's move on to the translation of y = |x + 3| + 1:
1. We start with the graph of y = |x|.
2. The expression x + 3 inside the absolute value function indicates a horizontal shift to the left by 3 units. This means we move the entire graph 3 units to the left.
3. Adding 1 outside the absolute value function indicates a vertical shift upward by 1 unit after the horizontal shift. So, we move the graph up by 1 unit.
By applying these transformations, we obtain the final translated graph, y = |x + 3| + 1.
Note: If you want to see the actual graph, you can plot the points by substituting different x-values into the equation and then connecting the plotted points.