Question

Which system matches the graph below?

1. y = 4x and y = 2x - 3
2. y = -4x and y = 2x - 3
3. y = -4x and y = 2x + 3
4. y = -4-x and y = 2x - 3

Answer 1

y = -4^x and y = 2x - 3

Explanation:

LEts pick some points from the graph and check with each option

Lets pick two point from red graph

REd graph points are (0,-1) and (1,-4)

Lets plug in the point and check with our options

y = 4^x

(0,-1) plug in 0 for x and -1 for y

-1 = 4^0

-1 = 1 false

y = -4^x

-1 = -4^0

-1=-1 true

Now we check with one more point (1,-4)

y = -4^x

-4 = -4^1

-4=-4 its true . So equation of red graph is y=-4^x

Green graph points are (0,-3) (2,1)

y=2x-3

(0,-3) -----> -3 = 2(0) -3 ----> -3=-3 true

(2,1) --------> 1=2(2) -3 --------> 1=1 true

So equation of green graph is y=2x-3

Answer 2

Option 2

Explanation:

None of the systems shown in the statement match the image. Since the graph represented by a red line is an exponential of the form
`y = -4 ^ x`

None of the systems presented have a function of this style.

The system that is drawn in the graph:

`y = -4 ^ x`. and
`y = 2x - 3`.

Unless you write:

4x refers to
`4 ^ x`

In that case, the correct answer is:

`y = -4 ^ x` and
`y = 2x - 3`.

See that the green line intersects the y-axis in y = -3.

If you do x = 0 in the equation
`y = 2x - 3`. then

`y = 2(0) -3`

`y = -3`

There you can check that this function corresponds to the one shown in the graph.

The red line of the graph cuts to the y-axis in y=-1

When we make x = 0 in the function
`y = -4 ^ x` we ​​have
`y = -4 ^ (0)`

`y = -1`

Finally the correct option is option 2.