Question

Which system matches the graph below?

Answer 1

Answer

Option 2

Step-by-step 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.

Answer 2

Answer:

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

Step-by-step 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