In the x-y plane, the point (3,1) lies on the graph of the function g. if g(x) = a - 2 x^2, where a is a constant, what is the value of a ?

The points on the graph of a function are all of the form

In fact, the graph is composed by all points such that y is the image of x, as written above.

So, if lies on graph, it means that .

Since we know the expression for , we can plug the values:

We can solve for by adding 18 to both sides to get .

So, the expression for the function is

180

step-by-step explanation:

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: