a Begin by identifying where the equation intercepts the y-axis.
B
b Begin by identifying where the equation intercepts the y-axis.
C
c Begin by identifying where the equation intercepts the y-axis.
D
d Begin by identifying where the equation intercepts the y-axis.
A
a (3) y=x+3
B
b (5) y=- x^2
C
c (6) y=x^2+3
D
d (2) y=3x-1
Practice makes perfect
a To match the correct table of values with the correct equation, we should start by determining where it intercepts the y-axis. This tells us the function's constant, which happens when x=0.
From the table, we see that y= 3 when x=0, which limits the equations it could be to (3) and (6).
(3) y&=x + 3
(6) y&=x^2+ 3
Next, we have to determine if the function is linear or quadratic. If it is linear, the function will have a constant rate of change between consecutive numbers. Let's plot the points in the table of values.
Examining the diagram, we see that the data points follow a linear pattern, which means the table should be paired with (3) y=x+3.
b Like in Part A, we will begin by identifying where the function intercepts the y-axis.
From the table, we see that y=0 when x=0, which limits the functions it could be to (1), (4), and (6). Notice that when the constant is zero, its usually not written out.
(1) y&= x
(4) y&= x^2
(5) y&=- x^2
Like in Part A, we will plot the point in a coordinate plane.
Examining the diagram, we see that the data points make a parabola that opens downwards. This means the coefficient to x^2 must be negative, and therefore we should pair it with (5).
c Like in Parts A-B, we will begin by identifying where the function intercepts the y-axis.
From the table, we see that y= 3 when x=0, which limits the functions it could be to (3) and (6).
(3) y&=x + 3
(6) y&=x^2+ 3
However, we have already paired (3) with the first table and therefore we must pair this table with the remaining quadratic option, (6) y=x^2+3. For good measure, we will plot the points to make sure it resembles a parabola.
d Like in previous parts, we will identify where the function intercepts the $y\text{-}axis.
& ↓
& |c|c|c|c|c|c|c|
x & -3 & 4 & 2 & -2 & 0 & -10
y & - 10 & 11 & 5 & -7 & -1 & - 31
There is only one equation with a y-intercept of -1, and that is (2) y=3x-1. For good measure, we will plot the data points to make sure they resemble a linear equation.
