Question

Which of the following statements about reflecting periodic functions is correct? (1 point)
Responses

If f(x)=sinx
and g(x)=cos(−x)
, then g(x)
is a reflection of f(x)
across the y-axis.
If f(x)=sinx
and g of x is equal to cosine of negative x, then g of x is a reflection of f of x across the y-axis.

If f(x)=cosx
and g(x)=cos(−x)
, then g(x)
is a reflection of f(x)
across the y-axis.
If f(x)=cosx
and g of x is equal to cosine of negative x, then g of x is a reflection of f of x across the y-axis.

If f(x)=sinx
and g(x)=sinx
, then g(x)
is a reflection of f(x)
across the y-axis.
If f(x)=sinx
and g(x)=sinx
, then g of x is a reflection of f of x across the y-axis.

If f(x)=sinx
and g(x)−sin(−x)
, then g(x)
is a reflection of f(x)
across the x-axis.
If f(x)=sinx
and g of x minus sine of negative x, then g of x is a reflection of f of x across the x-axis.
Skip to navigation

Answer 1

Correct are statements 2 and 4.

- Reflection across the y-axis: g(x)=f(−x). For f(x)=cos x, g(x)=cos(−x)=cos x = f(−x), so (2) is true (cosine is even).
- Reflection across the x-axis: g(x)=−f(x). For f(x)=sin x, g(x)=sin(−x)=−sin x = −f(x), so (4) is true (sine is odd).