What can you say about the y values of the two functions f(x)=-5^x+2 and g(x)=-5x^2+2?
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Value of y , you mean Range of function.
For f(x) = -5^x + 2
as you know, 5^x is exponential function
it lies between 0 to ∞ .
e.g., 0 < 5^x < ∞
⇒ - ∞ < -5^x < 0
⇒ -∞ < -5^x + 2 < 2
∴Range of F(x) ∈ (-∞ , 2)
For f(x) = -5x² + 2
For any quadratic equation , ax² + bx + c ≥ -D/4a , if a > 0
And if a < 0 then, ax² + bx + c ≤ -D/4a
Here, D = 0 - 4(-5)(2) = 40
so, -5x² + 2 ≤ -40/4(-5) = 2
⇒ 5x² + 2 ≤ 2
Hence, Range ∈ (-∞, 2]
For f(x) = -5^x + 2
as you know, 5^x is exponential function
it lies between 0 to ∞ .
e.g., 0 < 5^x < ∞
⇒ - ∞ < -5^x < 0
⇒ -∞ < -5^x + 2 < 2
∴Range of F(x) ∈ (-∞ , 2)
For f(x) = -5x² + 2
For any quadratic equation , ax² + bx + c ≥ -D/4a , if a > 0
And if a < 0 then, ax² + bx + c ≤ -D/4a
Here, D = 0 - 4(-5)(2) = 40
so, -5x² + 2 ≤ -40/4(-5) = 2
⇒ 5x² + 2 ≤ 2
Hence, Range ∈ (-∞, 2]
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