Which function represents a reflection of f(x) = Three-sevenths(2)x over the x-axis?

g(x) = –Three-sevenths(2)x
g(x) = Three-sevenths(–2)x
g(x) = Three-sevenths (one-half)–x
g(x) = Seven-thirds(2)–x

Given:

The given function is

We need to determine the reflection of f(x) over the x - axis

Reflection over x - axis:

The translation rule to reflect over the x - axis is given by

Thus, applying the rule, the function becomes

Multiplying both sides of the equation by -1, we have;

This can be written as

Hence, the reflection of the function over the x - axis is

Thus, Option A is the correct answer.

is there answer choices?

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3