Question

Algebra 2: The functions f(x) = x2 – 3 and g(x) = –x2 + 2 are shown on the graph.

The graph shows f of x equals x squared minus 3, which is an upward opening parabola with a vertex at 0 comma negative 3 and a point at negative 1 comma negative 2 and a point at 1 comma negative 2. The graph also shows g of x, which is a downward opening parabola with a vertex at 0 comma 2 and a point at negative 1 comma 1 and a point at 1 comma 1.

Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?

y ≤ x2 – 3
y > –x2 + 2

Answer 1

The set of inequalities y ≤ x² - 3 and y > -x² + 2 do not have a solution

we have: f(x) = x² - 3 g(x) = -x² + 2

Next, we change the equations to inequalities as
y ≤ x² - 3 y > -x² + 2

To modify the graph, we then perform the following transformations: Shift the function g(x) down by 2 units Reflect across the x-axis Shift the function g(x) down by 3 units

After the modifications in (a), we have: y ≤ x² - 3 and y > -x² + 2

Next, we plot the graph of the inequalities From the graph of the inequalities, the curves of the inequalities have no point of intersection

Hence, the set of inequalities do not have a solution

Answer 2

Alright, Thank you! u up for one more?

Answer 3

ight

Answer 4

Thx

Answer 5

The f(x) has a degree of 1, hence it is linear in nature while g(x) is a polynomial function because of the third degree.

The key features that they have in common are the y-intercept, domain, and range

Linear and quadratic equations Linear equations are equations that has a degree of 1 while polynomial equations are equations that has a degree of 2 and above.

Given the following functions f(x) = –4x + 5 and; g(x) = x^3 + x^2 – 4x + 5

Since the f(x) has a degree of 1, hence it is linear in nature while g(x) is a polynomial function because of the third degree.

The key features that they have in common are the y-intercept, domain and range

Answer 6

Thank you. And to let you know the first one was wrong :(

Answer 7

damn

Answer 8

thx though.

Answer 9

second one seems right though

Answer 10

That one was wrong to. :(