Answer:
B) Both functions have a y-intercept of -2.
Step-by-step explanation:
Hi there!
<u>A) Both functions are always increasing.</u>
⇒ False
Let's first take a look at the given equation, . This is a linear equation, and it is organized in slope-intercept form:
. <em>m</em> is the slope and <em>b</em> is the y-intercept. When <em>m</em> is positive, it is always increasing.
In , 3 is <em>m</em>, and because it's positive, this line is always increasing on a graph.
However, when we take a look at the given graph, this isn't the case. It is decreasing for values of x below 0 (on the left side of the y-axis).
<u>B) Both functions have a y-intercept of -2.</u>
⇒ True
In the given equation , this is true. -2 is the y-intercept.
On the given graph, we can see that the graph intercepts the y-axis at -2, so this is also true for the graph.
<u>C) Both functions are symmetric about the y-axis.</u>
⇒ False
The given graph is symmetric about the y-axis, but the line is not. Any line that would be symmetric about the y-axis would be in the form , which isn't the case here with
.
has a slope.
<u>D) Both functions are linear relationships.</u>
⇒ False
Sure, is a linear equation, making it a line, but not the given graph. The graph does not resemble a straight line, so it is not a linear relationship.
I hope this helps!