Function Math Problems - Practice with Solutions

For f(x)=x^4-12x^3+6 find the following.
A)f'(x)
B)The slope of the graph of f at x=-2
C)The equation of the tangent line at x=-2
D)The value(s) of x where the tangent line is horizontal

pighead73283r 2022-11-20

Show that the roots of $x^{2} + b x + a c = 0$ are a times the roots of the quadratic $a x^{2} + b x + c = 0$ by using transformation of the function $f (x) = a x^{2} + b x + c$
Let $f (x) = a x^{2} + b x + c$ and $g (x) = x^{2} + b x + a c$
The graph of $y = g (a x)$ results from shifting the graph of $y = g (x)$ horizontally b a factor of $1 / a$
Does that mean $g (a x) = f (x)$ ?

kaltEvallwsr 2022-11-19

For positive functions f,g, if $g (x) = x \cdot f (x)$ , and $g^{'} (x) \geq 0$ , $g^{″} (x) \leq 0$ , is $f^{'} (x) \leq 0$ ?

Emmanuel Giles 2022-11-19

Rewrite in standard form and give the vertex
$f (x) = 2 x^{2} - 6 x$

Aaleeyah Israel2022-11-14

Types of Functions
Scientists are studying the population of a rare species of primates, known as a Javan gibbons, on the Raja Ampat Islands in Indonesia. They are studying the gibbons on three different islands, Batanta, Misool, and Salawati. The scientists studied the population growth and recorded the data in the table.
Years (x) Batana
B(x) Misool
M(x) Salawati
S(x)
0 2 20 38
1 6 120 81
2 18 420 124
3 54 920 167
4 162 1620 210
5 486 2520 253
What type of function is B(x), linear, quadratic or exponential? Justify your answer and show calculations to support your conclusion.
What type of function is M(x)? Justify your answer and show calculations to support your conclusion.
What type of function is S(x)? Justify your answer and show calculations to support your conclusion.
A white-handed gibbon population, represented by W(x), was recorded at a fourth location, starting in year three.
6. Of the functions B(x), M(x), and S(x), which function is the same type as W(x)? Justify your answer and show calculations to support your conclusion.

Years (x)	Batana B(x)	Misool M(x)	Salawati S(x)
0	2	20	38
1	6	120	81
2	18	420	124
3	54	920	167
4	162	1620	210
5	486	2520	253

inurbandojoa 2022-11-14

How many functions respect the equation $3 f (f (x)) - 7 f (x) + 2 x = 0$

Bayobusalue 2022-11-12

Your alarm clock is broken and always rings with a delay. For example, last night, you set your alarm for 7:30 AM but your alarm rang at 7:42 AM. However, the delay is not constant. After much data collection, you realize that the alarm clock’s delay time (in minutes) can be reasonably modeled as a continuous random variable T with $f (t) = c e^{- t / 15} for t \geq 0 and f (t) = 0$ otherwise.
Answer the following questions:
(a) What is the value of c?
(b) What is the mean delay?
(c) What is the variance in the delay?
(d) If you wanted your alarm to ring at 7:30 AM, approximately what time should you set your alarm so that 95% of the time, the alarm rings before 7:30 AM?

Annie French 2022-11-11

Find an open set V containing $(1, 1)$ such that $f |_{V} : V \to f (V)$ is bijective, where $f : R^{2} \to R^{2} & f (x, y) = (x y, x - y)$
My Question: Clearly $f (x_{1}, y_{1}) = f (x_{2}, y_{2}) ⟹ x_{1} y_{1} = x_{2} y_{2} & x_{1} - y_{1} = x_{2} - y_{2}$ , thus $x_{1}^{2} + y_{1}^{2} = x_{2}^{2} + y_{2}^{2}$ . Hence both $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ are points of intersection of the same line and circle. But Then how do I find the open set V?

Humberto Campbell 2022-11-11

How to solve this recurrence relation $f (x, 0) = 3 x and f (x, n + 1) = f (f (x, n), n)$ and $f (x, 0) = 3 x and f (x, n + 1) = f (f (x, n), n)$ ?

Alexia Avila 2022-11-11

Find inverse function
$y = x^{2} - 12 x + 36$

Karley Castillo 2022-11-11

List all Df the possible rational zeroes for $f (x) = 2 x^{8} - 3 x^{6} + 8 x^{5} - 5 x + 6$

Jared Lowe 2022-11-10

Suppose a musical theater producer uses the rule $f (x) = - 360 x^{2} + 3600 x$ to estimate the musical's income (U) in dollars as a function of ticket price in dollars

Uriah Molina 2022-11-08

Let $A = [0, 1), B = (0, 1], C = (0, 1)$
Prove A is of cardinality equal to B by using Glueing Lemma to 'glue together' the identity function idC and some appropriate bijective function.

Kareem Mejia 2022-11-06

Convert $f (x) = (\cos x + \sin x) (1 - \sqrt{3} \tan x)$ into the form of $k (1 + \tan x) \cos (x + a) .$

figoveck38 2022-11-06

A function f has the form
$f (x) = a + b l n x .$
Find f if it is known that f(1) = 9 and $f (2) = 13.1$

Uriah Molina 2022-11-05

Let $f : R ⟶ R$ be a differentiable function. If
$lim_{x \to \infty} \frac{f (x)}{x} = 1,$
then there exists a sequence $(x_{n})$ such that $x_{n} \to \infty$ as $n \to \infty$ and
$lim_{n \to \infty} f^{'} (x_{n}) = 1.$
We tried to use the Mean Value Theorem. For each n, there exists $x_{n} \in [0, n]$ such that
$f^{'} (x_{n}) = \frac{f (n) - f (0)}{n} .$
Hence, $lim_{n \to \infty} f^{'} (x_{n}) = 1$ . But, we are not sure that $x_{n} \to \infty$

Nicholas Hunter 2022-11-05

Find the inverse of the following functios
$f (x) = 6 + 2^{7 x - 1}$

Nola Aguilar 2022-11-04

Let f be a function $f : R \to R$ , $f (x) = 4 x^{3} + 1$

Laila Murphy 2022-11-04

Describe the end behavior of the graph of the function $f (x) = - 5 (4)^{x} - 10$

limunom623 2022-11-03

I want to find the range of this function.
$f (x) = \frac{\tan^{2} (x) - 1}{\tan (x)}$

Dealing with function Math questions is never easy as these can be implemented virtually anywhere where Algebra is used. It means that starting with at least one function Math example from what has been provided below will help you. Of course, certain function Math problems will require more analysis and verbal explanations, yet these are also encountered as you look through the questions. Learn about the use of equations first! The functions Math problems are always based on the analytical part because the function Math equation always has only one answer for every unknown variable.

Algebra I

Functions in Algebra Examples