What is the limit of the function?

f(x)=4x8−3x7+2x−11

select true or false for each statement.

limit statement true false
limx→−∞f(x)=∞
limx→∞f(x)=−∞

The true and false statements concerning the limit of the function is:

The given function is:

To find , substitute into f(x)

To find , substitute into f(x)

Therefore:

For

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Step-by-step explanation:

The function in question is f(x) = 4x^8 - 3x^7 + 2x - 11.  The 4x^8 term is the dominant one when we focus on limits at plus or minus infinity.  For all practical terms this f(x) is f(x) = 4x^8, an even power of x.

Limit statement #1:  limx→−∞f(x)=∞ looks like 4(−∞)^8, which works out to +∞.  The first limit statement is thus true.

Limit statement #2:  limx→−∞f(x)=∞ looks like 4(∞)^8, which works out to +∞

The second limit statement is thus false.

f

step-by-step explanation:

f

y=mx+b

step-by-step explanation:

m slope, b y-intercept