Relations and Functions
Problem 1
x =
Five points:
y = 1 => x =
y = 2 => x =
y = 5 => x =
y = 10 => x =
y = 17 => x =
The x-intercept is at the point where y = 0.
y = 0 => x = not real number => no x - intercept
The y-intercept is at the point where x = 0
0 = => y = 1
The x-intercept and start point are at the point (0, 1).
Our graph is the right half of the open upward parabola that is shifted one unit upward.
The domain is
The range is
Since our relation passes the vertical line test, it is a function.
To shift our graph three units upward, we should subtract 3 from y.
After the transformation, our equation is
x =
To shift our graph four units to the left, we have to subtract 4 from x.
After the transformation, we have
x =
Problem 2
y = 3(x + 2)2 - 6
Five points:
x = 0 => y = 3(0 + 2)2 - 6 = 3 * 4 - 6 = 12 - 6 = 6
x = -1 => y = 3(-1 + 2)2 - 6 = 3 * 1 - 6 = 3 - 6 = -3
x = - 2 => y = 3(-2 + 2)2 - 6 = 3 * 0 - 6 = -6
x = -3 => y = 3(-3 + 2)2 - 6 = 3 * 1 - 6 = 3 - 6 = -3
x = -4 => y = 3(-4 + 2)2 - 6 = 3 * 4 - 6 = 12 - 6 = 6
To find the x-intercept we equate y to zero.
y = 0 => 3(x + 2)2 - 6 =0 3(x + 2)2 = 6 => (x + 2)2 = 2 => x + 2 = =>
x =
There are two x-intercepts => (
To find the y-intercept we equate x to zero
y = 3(0 + 2)2 - 6 = 12 - 6 = 6
The y-intercept is at the point (0, 6).
The vertex is at the point (-2, -6).
Our graph is the parabola. It opens upward, and it is shifted two units to the left and six units downward. It is also vertically stretched.
The domain is
The range is
As our graph passes the vertical line test, it is a …
