Sums and Products of Functions and Addition of Ordinates (VCE SSCE Mathematical Methods): Quizzes

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Sums and Products of Functions and Addition of Ordinates
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What is the rule for the sum of two functions ff and gg?

(f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x)

What is the rule for the product of functions ff and gg?

(fg)(x)=f(x)×g(x)(fg)(x) = f(x) \times g(x)

What is the domain of (f+g)(f + g)?

dom f∩dom g\text{dom } f \cap \text{dom } g

What does the symbol ∩\cap represent in domain notation?

Intersection

In coordinate geometry, what does the term 'ordinate' refer to?

The yy-coordinate

If both f(x)f(x) and g(x)g(x) are positive, how does (f+g)(x)(f + g)(x) compare to f(x)f(x)?

(f+g)(x)>f(x)(f + g)(x) > f(x)

When f(x)=0f(x) = 0, what does (f+g)(x)(f + g)(x) equal?

g(x)g(x)

For f(x)=cos⁡xf(x) = \cos x and g(x)=e−xg(x) = e^{-x}, what is (f+g)(0)(f + g)(0)?

22

For f(x)=cos⁡xf(x) = \cos x and g(x)=e−xg(x) = e^{-x}, what is (fg)(0)(fg)(0)?

11

If both f(x)f(x) and g(x)g(x) are negative, how does (f+g)(x)(f + g)(x) compare to g(x)g(x)?

(f+g)(x)<g(x)(f + g)(x) < g(x)

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