Question

Which function is increasing on the interval (-∞, ∞)

Answer 1

Differentiating each function, we have for all x, unless otherwise indicated,

$h(x) = 2^x - 1 \implies h'(x) = \ln(2) \, 2^x > 0$

$g(x) = -4 (2^x) \implies g'(x) = -4 \ln(2) \, 2^x < 0$

$f(x) = -3x+7 \implies f'(x) = -3 < 0$

$j(x) = x^2 + 8x + 1 \implies j'(x) = 2x + 8 > 0 \text{ only when } x > -4$

and only h(x) has a strictly positive derivative. (A)