Question

The degree of the function f(x)=-(x+1)^2(2x-3)(x+2)^2 is blank, and it’s y intercept is ( ) blank

Answer 1

Part A: The degree of the function f(x) = 5

Part B: y-intercept of f(x) = 12

Step-by-step explanation:

Part A: Find the degree of the function.

The degree of the function is the greatest exponent of x

Given: f(x) =-(x+1)²(2x-3)(x+2)²

So, (x+1)² = x² + 2x + 1

(2x-3) = 2x - 3

(x+2)² = x² + 4x + 4

∴ the greatest exponent of x = x² * 2x * x² = 2 x⁵

So, the degree of the function f(x) = 5

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Part B: Find y-intercept of the function.

y-intercept is the value of y at which x = 0

For the given function f(x) = f(x)=-(x+1)²(2x-3)(x+2)²

When x = 0

f(x) = -( 0 + 1 )²( 2 * 0 - 3 )( 0 + 2 )²

= -(1)² (-3) (2)²

= -1 * -3 * 4 = 12

So, y-intercept of f(x) = 12