Question

Given a polynomial function f(x) = 2x2 – 3x + 5 and an exponential function g(x) = 2% – 5, what key features do f(x) and g(x) have in common?
A. Both f(x) and g(x) have the same domain of (0, -60).
B. Both f(x) and g(x) have the same range of [0,-).
C. Both f(x) and g(x) have the same x-intercept of (2,0).
D. Both f(x) and g(x) increase over the interval of (-4,-).

Answer 1

A. Both $f(x)$ and $g(x)$ have the same domain of $(9, +\infty)$.

How to analyze similarities in two functions

In this question we must analyze the domain, range, x-intercepts and increase intervals:

Domain

$Dom \{f(x)\} = \mathbb{R}$

$Dom \{g(x)\} = \mathbb{R}$

Both functions are continuous.

Range

$Ran \left\{f(x)\right\} = (3.875, +\infty)$

$Ran \{g(x)\} = (-5, +\infty)$

x-Intercepts

$f(x):$ $(x,y) = \emptyset$

$g(x):$ $(x,y) = (2.322, 0)$

Increase intervals

$f(x):$ According to the graph, $f(x)$ increase over the interval of $(3.875, + \infty)$.

$g(x) :$ According to the graph, $g(x)$ increase over the interval of $\mathbb{R}$

After a quick analysis, we conclude that option A offer the best approximation to characteristics of both functions. $\blacksquare$

Remark

The statement presents mistakes and is poorly formatted. Correct form is:

Given a polynomial function $f(x) = 2\cdot x^{2}-3\cdot x + 5$ and an exponential function $g(x) = 2^{x}-5$. What key features do $f(x)$ and $g(x)$ have in common?

A. Both $f(x)$ and $g(x)$ have the same domain of $(9, +\infty)$.

B. Both $f(x)$ and $g(x)$ have the same range of $(-\infty, 0]$.

C. Both $f(x)$ and $g(x)$ have the same x-intercept of $(2,0)$.

D. Both $f(x)$ and $g(x)$ increase over the interval of $(-4, +\infty)$.

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