Exponential and Logarithmic Functions

INCORRECT. Both functions are quadratic.

INCORRECT. Both functions pass through the origin (0,0).

INCORRECT. Both functions have a constant slope.

CORRECT. Both functions are one-to-one.

It must be one-to-one (bijective)

It must have an asymptote at y=0

It must have a positive slope everywhere on its domain

It must intersect the origin (0,0)

It turns into '1/a'.

It becomes '10'.

It changes to 'e'.

It remains 'a'.

Suggests isolating the variable exp(b*x+c) first, then deconstructing sequentially until reverse-engineered fully back to the terms initial input encompassed primarily via antecedent stages involved thus far.

Proposes utilizing transcendental manipulations complex enough to transcend basic polynomial arithmetic yet simple enough to maintain the integrity of the overarching system design while converting the process in the opposite direction entirely compared to the beginning status it stood at the start once the reversal was initiated, proper course of action taken place consequently.

It implies solving the equation relative to “y,” yielding the form $g(y)=\frac{\ln\left(\frac{y-d}{a}\right)-c}{b}$, assuming parameters permit valid solutions existent within the operational context required thereof.

Indicates direct inversion methodology whereby coefficients/factors switched reciprocally around until orderly arranged in the opposite manner/fashion compared to the starting setup initially presented before reversing the sequence began onwards after.

The slope remains constant

The slope becomes increasingly negative

The slope approaches zero

The slope rapidly approaches infinity

Q(0) = 15 grams

Q(0) = 20 grams

Q(0) = 40 grams

Q(0) = 10 grams

Each contains exactly one type of discontinuity, which manifests differently due to their inverse relationship

While $b^x$ is always continuous, $\log_b(y)$ exhibits a countable infinity of removable discontinuities over its domain

Both functions are continuous over their respective domains without exception

They might share identical vertical asymptotes demonstrating mutual points of discontinuity

t=7 since this would make inside term zero

t=9 since this would make inside term undefined

t=13 since this makes denominator zero in equivalent rational expression

None, because $t^2 - 6t + 14 \geq 8$ for all t

$g(x)=5^{-0.25x}$

$g(x)=(0.5 \\times 5)^{-0.5x}$

$g(x)=10^{-0.5x}$

$g(x)=5^{-0.5(0.5x)}$

$y = \frac{2}{x}$

$y = \log_{2}(x)$

$y = \frac{x}{2}$

$y = x^2$