Question

Given that f(x) = Cax for some positive constants C and a, sketch the graph of this exponential function if you also know that the y−intercept is at 2 and that the curve goes through the point (2, 32). Determine the values of C and a and then ﬁnd f(1.4), rounding your result to one decimal.

Answer #1

Suppose f(x)=ax^3−x^2+c where a and c
are some positive constants. Then
f(x) is concave up for x in....?

Sketch the graph of a function f that is continuous on (−∞,∞)
and has all of the following properties:
(a) f0(1) is undeﬁned
(b) f0(x) > 0 on (−∞,−1)
(c) f is decreasing on (−1,∞).
Sketch a function f on some interval where f has one inﬂection
point, but no local extrema.

Given the polynomial function f(x)=(x-a)(x-b)^2, and
a<0<b, find the following:
A). Sketch the graph
B). find the x and the y intercepts
C). find the solution to f(x)<0
D). find the solution to f(x) is greater than or equal to 0

Graph: f(x)= 2
Find (a) The domain of f.
(b) All asymptotes (write the equations)
(c) X- intercept(s), Y- intercept. Write them as ordered
pairs.
(d) Graph the function. Include asymptotes

Find traits and sketch the graph the equation
for a function g ( x ) that shifts the function f ( x ) = x + 4 x 2
− 16 two units right. Label and scale your
axes.
Domain:
x – Intercepts:
y – Intercept:
Vertical Asymptotes:
Holes:
End Behavior:
Range:

Consider the quadratic function f, given by f(x) = −x2 + 6x−8.
(i) Determine if the graph of y = −x2 + 6x − 8 is concave up or
concave down, providing a justiﬁcation with your answer. (ii)
Re-write the equation of the quadratic function f, given by f(x) =
−x2 +6x−8, in the standard form f(x) = a(x−h)2+k by completing the
square. Hence determine the vertex of the graph of y = f(x).
(iii) Identify the x-intercepts and y-intercept...

Question 1a Consider the polynomial function P(x) = x3+x2−20x.
Sketch a graph of y = P(x) by: determining the zeros of P(x),
identifying the y-intercept of y = P(x), using test points to
examine the sign of P(x) to either side of each zero and deducing
the end behaviour of the polynomial.
b Consider the quadratic function f(x) = 2x2 + 8x−1. (a) Express
f(x) in standard form. (b) Determine the vertex of f(x). (c)
Determine the x- and y-intercepts...

Sketch the graph of the function f(x) = x − 4 / x + 4 using the
guidelines below, a. Determine the domain of f.
b. Find the x and y intercepts.
c. Find all horizontal and vertical asymptotes.
d. Determine the intervals of increasing/decreasing.
e. Determine the concavity of f.

For the function f(x) = ? 3−1 ? 2−9 , find any slant asymptotes
and sketch the graph by finding any vertical asymptotes, horizontal
asymptotes, x intercepts, y intercept.

Consider function f(x, y) = x 2 + y 2 − 2xy and the 3D graph z =
x 2 + y 2 − 2xy. (a) Sketch the level sets f(x, y) = c for c = 0,
1, 2, 3 on the same axes. (b) Sketch the section of this graph for
y = 0 (i.e., the slice in the xz-plane). (c) Sketch the 3D
graph.

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