Which comparison is correct for the values of f(x) and g(x) when x = -3
function a : f(x) = -x^2 +4
function b

a. f(-3) < g(-3)
b. f(-3)> g (-3)
c. f(-3) = g(-3)

A) g(-3) < g(-3)

Step-by-step explanation:

Given: f(x) = -x^2 + 4

When x = -3, f(-3) = - (-3)^2 + 4

Now we have to simplify it.

f(-3) = -9 + 4

f(-3) = -5

Now we have to find g(-3) from the given table.

When x = -3, g(-3) = 1 from the given table values.

We found f(-3) = -5 and g(-3) = 1

Here -5 < 1

Therefore, f(-3) < g(-3)

Answer is A) g(-3) < g(-3)

Hope you will understand the concept.

Thank you.

Choice A is the answer.

Step-by-step explanation:

We have given the values of function and a equation of function.

f(x) = -x² +4

We have to find the relation between both function when x = -3.

From table, we observe that

g(-3) = 1

Now, Putting x = -3 in f(x), we have

f(-3) = -(-3)²+4

f(-3) = -9+4

f(-3) =  -5

Hence, -5 < 1

f(-3) < g(-3) which is the answer.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

probably .5

i can on others if necessary.