Question

I only really need the domain and range, intervals, and end behavior. My Precalculus class never covered piecewise functions so any help is much appreciated. Thanks so much

Answer 1

(a)

Domain:

we know that domain is all possible values of x for which any function ios defined

Here, curve is defined for all values of x

so, domain is

$(-\infty,\infty)$

Range:

Range is all possible values of y for which x is defined

minimum value of y is -4

maximium value of y is +inf

so, range is

$[-4,\infty)$

(b)

x-intercept:

It is the value of x where f(x)=0

so, the point where curve intersects on x-axis

and we get

$2x^2-4=0$

$x=\sqrt{2}$

and

$x=-5$

(c)

Increasing interval:

where curve is moving upward

we can see that

$(0,\infty)$

Decreasing interval:

where curve is moving downward

we get

$(-\infty,-1)U(-1,0)$

Constant:

constant means horizontal line

there is no horizontal line here

so, it does not exist

(D)

End behavior:

when x-->+inf

y is moving upward

so, y---->+inf

when x-->-inf

y is moving upward

so, y---->+inf

(E)

we can see that curve jupms at x=-1

so, there is discontinuity at x=-1

and this is jump type of discontinuity

(F)

For odd:

f(-x)=-f(x)

For even:

f(-x)=f(x)

we can see that none of them holds true

so, this is neither