Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Check all that apply. The domain is {x|x ≤ –2}. The range is {y|y ≤ 6}. The function is increasing over the interval (–∞ , –2). The function is decreasing over the interval (−4, ∞). The function has a positive y-intercept.
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f(x) = -x² - 4x + 2,
This function is defined for all real numbers .
∴ domain ∈ R
Range of this Function :
f(x) = - x² - 4x + 2 ≤ -(-4² - 4 × 2 × (-1) )/4(-1)²
f(x) ≤ 24/4
f(x) ≤ 6
∴ range is {y|y ≤ 6}
f(x) = - x² - 4x + 2 ,
differentiate with respect to x
f'(x) = -2x - 4
∴ 2x = -4 ⇒ x = -2
we know, function is decreasing in [a,b] when f'(x) < 0 in [a, b]
function is increasing in [ a, b] when f'(x) > 0 in [a, b]
function is decreasing, in interval x ∈ ( -∞ , -2 )
function in increasing , in interval x ∈ [-2 , ∞ )
This function is defined for all real numbers .
∴ domain ∈ R
Range of this Function :
f(x) = - x² - 4x + 2 ≤ -(-4² - 4 × 2 × (-1) )/4(-1)²
f(x) ≤ 24/4
f(x) ≤ 6
∴ range is {y|y ≤ 6}
f(x) = - x² - 4x + 2 ,
differentiate with respect to x
f'(x) = -2x - 4
∴ 2x = -4 ⇒ x = -2
we know, function is decreasing in [a,b] when f'(x) < 0 in [a, b]
function is increasing in [ a, b] when f'(x) > 0 in [a, b]
function is decreasing, in interval x ∈ ( -∞ , -2 )
function in increasing , in interval x ∈ [-2 , ∞ )
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