Answer: +∞ ..... +∞ ..... -15 ..... 0, -3, 5 ..... 1 ..... 2 ..... 1 ..... -112
<u>Step-by-step explanation:</u>
f(x) = x²(x + 3)(x - 5)
How many exponents does "x" have? <em> x², x, x = x⁴</em>
Since the exponent is even, it is an even function. So, the end behavior of the right and left sides will be the same. Since it is positive, the right hand side will go to positive infinity, therefore, the left hand side will also go to positive infinity.
What is the constant (multiply the numbers that don't have a variable)? This is the y-intercept. <em> 3(-5) = -15</em>
Set the function equal to zero to find the x-intercepts. Use the zero product propertty to solve (set each factor equal to zero). These are the roots.
x²(x + 3)(x - 5) = 0
x² = 0 (x + 3) = 0 (x - 5) = 0
x = 0 x = -3 x = 5
middle far left far right
M = 2 M = 1 M = 1
f(4) = 4²(4 + 3)(4 - 5)
= 16(7)(-1)
= -112
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Answer: C
<u>Step-by-step explanation:</u>
The only graph that has the end behavior of both left and right sides going to positive infinity is graph C. You can also confirm that graph C has the zeroes of -3, 0, and 5 where x = 0 is a double root (touches) and the others cross.
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Answer: even ..... negative
<u>Step-by-step explanation:</u>
This is the same explanation as the first question:
End behavior is the same so even function.
Right hand behavior goes to negative infinity so the leading coefficient is negative.
