Question

A) F(x)=3+8x^2 б) F(x)=1/x+sinx в) F(x)=x^4cosx г) F(x)=2x-3/3+x д F(x)=(6-5x)^4

Answer 1

Оставшееся решение 8-ой :

Answer 2

To analyze the given functions, I will provide information about their properties and characteristics. I'll go through each function one by one:

A) F(x) = 3 + 8x^2

• This is a polynomial function of degree 2 (quadratic function).
• The leading term is 8x^2, which has a positive coefficient, indicating that the function opens upwards.
• The function has a constant term (3), which means the graph intersects the y-axis at the point (0, 3).
• The graph is a parabola with its vertex at the point (0, 3).
• There are no vertical asymptotes or holes in the graph.

б) F(x) = 1/x + sin(x)

• This function is a sum of two separate functions: 1/x and sin(x).
• The first part, 1/x, represents a hyperbola. It has a vertical asymptote at x = 0 and approaches zero as x moves toward positive or negative infinity.
• The second part, sin(x), is a periodic function with amplitude 1, oscillating between -1 and 1 infinitely in both positive and negative directions.

в) F(x) = x^4 * cos(x)

• This is a product of two functions: x^4 and cos(x).
• The term x^4 represents a polynomial function of degree 4, which means the graph may have up to 4 real roots.
• The term cos(x) is a periodic function with amplitude 1, oscillating between -1 and 1.

г) F(x) = (2x - 3)/(3 + x)

• This is a rational function.
• The function has a vertical asymptote at x = -3, where the denominator becomes zero.
• The graph has a horizontal asymptote as x approaches positive or negative infinity, which is y = 2.
• The function can have a horizontal intercept when the numerator equals zero (2x - 3 = 0), at x = 3/2.

д) F(x) = (6 - 5x)^4

• This is a polynomial function of degree 4.
• The leading term is -5x^4, which has a negative coefficient, indicating that the function opens downwards.
• The graph intersects the y-axis at the point (0, 6^4) = (0, 1296).
• There are no vertical asymptotes or holes in the graph.

Keep in mind that without specific ranges or context, the graphs and behaviors of these functions can vary. To get a more precise understanding or to sketch their graphs, it's essential to use a graphing calculator or plot them manually.