Could you please check my work.
Determine whether the realtion is a funtion.
2.{(-6,2),(-2,5),(3,2),(3,-7)} -Not a function
2. Determine whether the equation defines y as a function of x.
2x+4y=15- the answer I got is y is a ntion of x.
Evalute the function at the given value of the independent variable and simplify.
f(x)=2x^2-5x+6; f(x-1)- I got 2x^2-9x+13
Graph the given functions on the same retangular coordinate system. Described how the graph of g is realted to the graph of f.
f(x)=2x^2, g(x)=2x^2-3- Once I graphed it I got that g shifts the graph of f vertically down 3 units.
Recheck the evaluate the function question.
1. To determine whether a relation is a function, you need to check if each input (x-value) is associated with only one output (y-value). In the given relation, we have:
{(-6,2), (-2,5), (3,2), (3,-7)}
Since the x-value of 3 is associated with two different y-values (2 and -7), this relation is NOT a function.
2. To determine whether the equation defines y as a function of x, you need to check if solving the equation for y will give you a unique value for y for every value of x. In the given equation:
2x + 4y = 15
You can solve for y as follows:
4y = 15 - 2x
y = (15 - 2x) / 4
y = (15/4) - (1/2)x
Since y can be uniquely determined for every value of x, the equation defines y as a function of x.
3. To evaluate the function at a given value of the independent variable (x) and simplify, substitute the given value into the function equation and simplify. In the given function:
f(x) = 2x^2 - 5x + 6
To evaluate f(x-1), substitute x-1 for x:
f(x-1) = 2(x-1)^2 - 5(x-1) + 6
= 2(x^2 - 2x +1) - 5x + 5 + 6
= 2x^2 - 4x + 2 - 5x + 5 + 6
= 2x^2 - 9x + 13
Therefore, after simplifying, f(x-1) is equal to 2x^2 - 9x + 13.
4. To graph two functions on the same rectangular coordinate system, plot the points representing the x and y values for each function and then connect the points to form the graphs. In the given functions:
f(x) = 2x^2
g(x) = 2x^2 - 3
Both functions are quadratic functions and have the same coefficient for x^2. Thus, the graph of g is obtained by vertically shifting the graph of f downward by 3 units.