Find the coefficients a,b in the function f(x)=ax+b so that (f(x1)-y1)^2+(f(x2)-y2)^2+(f(x3)-y3)^2 is as small as possible, where {(x1,y1),(x2,y2),(x3,y3)}={(0,0),(1,0),(1,1)}. In other words, find the line of best fit (least squares regression) through those three points.

Q: A quadratic function is given f(x) = -x^2 + 8x + 4. The standard form  f(x) = -(x - 4)^2 + 20. The…

A: Use the given information and sketch the graph of the given function as follows.

Q: Let f(x)=9x+8‾‾‾‾‾‾√f(x)=9x+8 and g(x)=x+9g(x)=x+9 be functions from ℝR to ℝR. Find the following.…

A: We will find out the required values.

Q: If  f(x) = 3x + 1  and g(x)=4/x.find f(g(x)) and g(f(x)).

A: Given f(x)=3x+1 and g(x)=4x we have to find f(g(x)), g(f(x))

Q: Find the equation of the quadratic function f that has its vertex at (3, 5) and contains the point…

A: Given: vertex at 3,5 and it contain the point 2,3

Q: Determine the x-intercept(s) of the quadratic function f(x)=x²+ 2x+ 2. no x-intercept(s) (-7, 0),…

A:

Q: Let f(x) = 4+ (5x +9)³. Find f¹(x) = (1) · (√(x − 4) – 9) Find (ƒ(2)) -¹ = (¹) · (√(x-4) – 9)

A:

Q: Calculate Duf (2₁-4,1) in the direction of 9 = 2₁ +2²₁ +3k for the function f(x, y, z) = x² +…

A:

Q: = x? – 5x + 7 has roots a and B. Use symmetric Suppose that f(x) functions to find a + B, aß, a² +…

A: If we have a quadratic equation ax2+bx+c=0 and α and β are the roots then: α+β=-ba αβ=ca We can use…

Q: Why is .5x.5.x.5x.5x.5 =0.03125 But .5x4=2 And 54=0.03125 Aren't they all the same equations just…

A:

Q: Define f(x) = x2 + 2x-15 and g(x) = (√x+4)  (Note: x+4 all under square root) Give the value of…

A: We will find the value of (fg)(5) from the given information using the composition of functions.

Q: Show that the function g(x) = x³ – 7x² + 25x + 8 has exactly one real root- |

A: Given: gx=x3-7x2+25x+8 To show function gx has exactly one real root.

Q: Give the domain for t(x)= x+1/x2-3x-18

A: Given function is,

Q: Given f(x)= x^3 − 6x^2+9x, find the multiplicity of the zero at x = 3

A:

Q: Given that f(x) = x² – 7x and g(x) : (a) (f + g)( – 4)=| = x + 10, find (b) (f – 9)( – 4)= (c) (fg)(…

A:

Q: f(x) = 2x4 + 2x³ – x² + 2x +3 and g(x) = x + 1 find (승)(2) and (-4).

A: fgx=f(x)g(x)=2x4+2x3-x2+2x+3x+1

Q: Find the zeros of f(x) = x^2 − 6x + 10. Then, compute x1/x2 where x2 is the zero with positive…

A:

Q: If f(x+y) =f(x) +f(y) and f (1) =3, find f(2), f(3), and  f(4). Is f(x+y) =f(x) +f(y) for all…

A:

Q: Let f(x) -x² + x. Let g(x) = 6x - 4. Find the following: (a) f(5) + g(5) = 56 (b) f(6) g(6) = 1344…

A: The given functions are f(x)=-x2+x,g(x)=6x-4 We have to find the a) f(5)+g(5)b) f(6).g(6)c)…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: