Algebra

Algebra

Part 1

1) f(x) = 4

When x = -2

f(-2) = 4

When x = -1

f(-1) = 4

When x = 0

f(0) = 4

When x = 1

f(1) = 4

When x = 2

f(2) = 4

x

-2

-1

0

1

2

f(x)

4

4

4

4

4

The graph of this equation is a horizontal line intercepting the y-axis at point (0,4). Since the line is parallel to the x-axis, it does not intercept it. The reason for this is that the power of x in the equation is zero. Since the graph is a straight line, there is no vertex.

There is no start or end point since the graph can be extended to an indefinite point on both sides of the y-axis. The domain of the function is {x | x ?/R}. The range is {x = 4}. This is a function since it allows us to deduce something from the domain.

1) x = (y + 2)2

When y = -2

x = (-2 + 2)2

x = 0

When y = -1

x = (-1 + 2)2

x = 1

When y = 0

x = (0 + 2)2

x = 4

When y = 1

x = (1 + 2)2

x = 9

When y = 2

x = (2 + 2)2

x = 16

x

0

1

4

9

16

y

-2

-1

0

1

2

The graph formed by this equation is a downward sloping graph which intercepts the x-axis at point (4,0) and y-axis at point (0,-2). The position of the curve is on the center of the line with the vertex at point (0, -2) and sloping downwards. This means that this point is also the minima. The domain of the equation is {x | x ?/R}. This is also the range since there is no limit as the graph extends till infinity. This is not a function; it is an equation since the variables are dependent and in relation to each other.

Shifting of the Graph

Assuming that the first graph has shifted three point upwards and four points towards the left, the new equation of the graph will be:

f(x) = 7

The reason for this equation is that since the graph is a horizontal line perpendicular to the x-axis, any horizontal movement will not affect the function. However, any vertical movement will cause the constant to change with respect to the new position of the graph. The domain of the graph will remain the same.

Part 2

(f - h)(4)

= f(4) - h(4)Each can be evaluated separately and then subtracted

f(4) = 2(4) + 5

f(4) = 8 + 5

f(4) = 13

h(4) = (7-4) / 3

h(4) = 3 / 3

h(4) = 1

f(4) - h(4) ...