Let f(x) = x 2 + 2x - 21. (a) Show that the lines y = 3x - 25, y = 6x - 25, and y = 9x - 25 intersect the graph off in zero, one, and two points, respectively. (b) Sketch the graph off and the three lines from (a)

Q: Find f(x)=x-8/6x-1 and find the equation of the line tangent to the graph of f at x=2. and what is…

A:

Q: Find the slope of the secant line to the function f(x)=4x²- 3x, through point P, where x= - 1, and…

A: To find the slope of secant line PQ to  the function f(x)

Q: Graph the function y = x2 over the interval [-2, 2].

A: y=x2 We first make a table for the function x -2 -1 0 1 2 y 4 1 0 1 4

Q: let f(x)=0.5x2-5 find the slope of the secant line through (2,f(2)) and (4,f(4))

A: Let f(x)=0.5x2-5. We need to find the slope of the secant line through (2,f(2)) and (4,f(4)). Here,…

Q: 2) y=-5+ Vx+ 1

A:

Q: Determine whether there exists a constant c such that the line x + cy = 1: passes through (3, 1).

A: We have to determine the value of constant c such that the line x+cy=1 is passing through the point…

Q: find the point at which the line g(x)=−1x+0g(x)=-1x+0 intersects the line k(x)=−4x+9

A:

Q: Find the point at which the line f(x) = - 2x +4 intersects the line g(a) = -a

A: Given, f(x)=-2x+4 and g(x)=-x

Q: Sketch the graph of y = f (x + 2) − 1, where f (x) = x2 for −2 ≤ x ≤ 2.

A: To sketch the graph

Q: Suppose that the x intercepts of the graph of y=f(x) are -5 and 3. What are the x intercepts of the…

A:

Q: Find the equation of the line tangent to the graph of f(x)=5x^{3}+6x^{2}-6x-3

A: This question is related to functions, We will solve it using given information.

Q: sketch the graph and draw several vertical and horizontal traces. f (x, y) = 4 − x2 − y2

A: f(x,y)=4-x2-y2

Q: Use the graph of y = f(x) to graph y = f(-x) + 3. (0, 4) (3, 2) (-2, 0) 1- -4-3-2-1, 2 3 4 -2- -3.…

A: Given graph: y=f(x) We need to graph y=f(-x)+3

Q: For the function f(x)=2x^{2}+4x-1f(x)=2x2+4x−1, find the slope of the secant line between x=-1x=−1…

A:

Q: Sketch the graph of the relation R= {(x, y)|x² – 2x- 2 < y< 2x – r² + 2}.

A:

Q: Find the equation of line (L) that passes through the intersection point of the two functions y = v2…

A: In this question given that two line which are intersect each other and and a line is perpendicular…

Q: Q1/a) Find the curve whose slope at the point (x,y) is 3x2 if the curve is also passes through the…

A:

Q: х3 — х2 — 12х x - - Sketch the graph of y = f(x) | ,2 x* - х — 2

A:

Q: The graph of y =f(x+3)  is obtained from the graphof y = f(x) by shifting_________ 3 units.

A: Given, y =f(x+3)

Q: Determine the point on the curve for the function H(x)=(-5x+7)(2x+3) where the slope is -1/2

A:

Q: Let c be a fixed constant. Explain the relationship betweenthe graphs of: y = f (x + c) and y = f…

A: To explain: The relation between the graphs of y=fx+c and y=fx in rectangular coordinates. Concept…

Q: Find the slope of the graph of y = f(x) at the designated point. %3D f(x) = 2x - 7x +5; (3,2) The…

A: To find the slope of graph of y = f(x) at (3,2)

Q: Find the point at which the line f(x) = – x – 2 intersects the line g(x) = 3x + 6

A:

Q: what is the slope of the curve

A:

Q: 4) y= V4x + 8 -2 9-

A:

Q: Graph the function f(x) = x + 4x - 12 on the coordinate plane. %3D y 6- 2+ 一 -18 -16 -14 -12-10 -8…

A:

Q: If f(x) = ax4 + bx3 + cx2 + dx + e, determine a, b, c, d and e so that the graph of f will have a…

A:

Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line.…

A:

Q: If f(x)=3x^2-2, and g(x)=f−1(x), what is the slope of the curve g(x)=f−1(x) at the point (10, 2)

A: Given f(x) =3x²-2  And g(x)=1-f(x) =1-(3x²-2) =1-3x²+2 g(x)=-3x²+3 For slope of curve g(x)…

Q: Draw the graph of f(x) = 4ª -4 10+ 5- 4 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 I 2 3 4 5 6 7 8 -2- -3 -4…

A: We have to draw the graph of  f(x)=4x-4.

Q: Where does the graph of fx equal 3e^x-x/2 have a horizontal position

A: A function takes a horizontal position at a point where x=a if f'(a)=0.

Q: 5. Sketch the graph of v: R ® R, v(x) = 2x² – 5x – 3, indicating the X- and y-intercepts, and the…

A: Given: v(x)= 2x2-5x-3.

Q: A market analyst working for a small appliance manufacturer finds that if the firm produces and…

A: we are given with profit equation  Lets graph the given equation  the x intercepts are (-45.224,0)…

Q: Consider the function f(x) = 6x + x² and the point P(-2, -8) on the graph of f. (a) Graph f and the…

A: This is a question related to slope of the line passing through two points. The general equation for…

Q: The slope y-intercept form of a linear relation is represented by y=mx+by=mx+b.  Which equation…

A: Solution: The objective is to find equation shows x isolated correctly for this formula

Q: Sketch the curve: f(x) = x^4 - 6x^2

A: solution:-f(x)=x4-6x2Domain=(-∞, ∞)x-interceptsy=f(x)=0f(x)=x4-6x2=0x2x2-6=0x2(x+6)(x-6)=0(x+6)=0,…

Q: Find the slope of the graph of the function x2+y2=xy+1/4 at (1/2 , 1/2)

A: Given function is Differentiating both sides with respect to x, we get

Q: 3.Find the coordinates of the points on the curves y =x3 -3x2-12x+10 with the gradients -2.

A:

Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line.…

A: The given function is f(x)=2x2 and the line is 6x-y+3=0. The objective is to obtain an equation of…

Q: Find the point at which the line f(x)=−5x−3f(x)=-5x-3 intersects the line g(x)=−x+1g(x)=-x+1

A: The given functions are fx=-5x-3gx=-x+1

Q: Find the gradient of the graph a) y = 6-3x where x = 5 )y= 12 + x-3x? where x = - 3

A: Find the gradient of the function

Q: Find the point at which the line f(x) = - 3x +8 intersects the line g(x) = -5z + 16 %3D %3D

A: Given f(x)=-3x+8 g(x)=-5x+16

Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line.…

A: Here we find equation of a line that is tangent to the graph fx=x2 and parallel to the line…

Q: Determine the intercepts of the graph of f(x) = -4x - and 0, 16 (3,0) and 0, and 0, 16 0 and 0, 16 O…

A: Please refer the attached image for complete solution.THANK YOU.

Q: The graph of a function y = f(x) in the xy-plane is the set of all points _______ that satisfy the…

A: Given: The graph of a function y = f(x) in the xy-plane is the set of all points _______ that…

Q: The axis of symmetry of the graph of f(x) = −2x² − 4 is the line y = 0. - Select one: True False

A: Given that the axis of symmetry of the graph of fx=-2x2-4 is the line y=0.

Q: y=4x

A: Linear function is given by equation y=4x. we have to show that value of y increases by 4 between…

Q: Sketch the graph of f(x)=(x+2)³/²+1 stretch vertically by factor of 3.

A: Given: The function is, fx=x+23/2+1

Q: If f(x)=5x2, and g(x)=f−1(x), what is the slope of the curve g(x)=f−1(x)g(x)=f−1(x) at the point (5,…

A:

Q: Estimate the slope of the graph at x=0. AY 5- 4 2- -109 6 54 19 2345 6 7 8 9 10 -2 -4 -5- -2 O 1 O 2…

A: Given: The graph is To determine: The slope of the graph at x=0.

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.