How do you graph #y = |x| + 3 #?

Question

Ethan Adkins · Accepted Answer

Shift #y=abs(x)# up the y axis by 3 units.

graph{abs(x)+3 [-10., 10, -1.5, 15]}

Jace Anderson · Answer

undefined To graph the equation $y = |x| + 3$, we can start by recognizing that $|x|$ represents the absolute value of $x$, which means it will always be non-negative. So, $y$ will be equal to $x$ plus a constant value of 3.

To graph this equation, we can plot points on the coordinate plane. For $x < 0$, the absolute value of $x$ will be equal to $-x$. For $x \geq 0$, the absolute value of $x$ will be equal to $x$.

We can choose some values for $x$ and find corresponding values for $y$ to plot the points. For example, when $x = -2$, $y = |-2| + 3 = 2 + 3 = 5$. So, we have the point $(-2, 5)$. Similarly, when $x = 0$, $y = |0| + 3 = 0 + 3 = 3$, giving us the point $(0, 3)$. When $x = 2$, $y = |2| + 3 = 2 + 3 = 5$, resulting in the point $(2, 5)$.

Plotting these points and recognizing that the graph forms a V-shape with the vertex at the point $(0, 3)$, we can draw the graph accordingly. The graph will consist of two straight lines, one with a positive slope on the right side of the y-axis and one with a negative slope on the left side of the y-axis, meeting at the vertex $(0, 3)$.