Answer the question about the given function.

Question

f (x) = 2x² - x - 1

(a) Is the point (-1, 2) on the graph of f ?

(b) If x = - 2, what is f (x) ? What point is on the graph of f ?

(c) If f (x) = - 1, what is x? What point(s) are on the graph of f ?

(d) What is the domain of f ?

(e) List the x-intercepts, if any, of the graph of f.

(f) List the y-intercept, if there is one, of the graph of f.

Answer 1

Step 1:

The function and the point .

(a)

The point should satisfies the function .

Substitute in the function.

.

Hence, the point is on the graph of function .

Step 2:

(b)

Find .

The function .

Substitute in the function.

.

Hence, the point is on the graph of function .

Solution :

(a) The point is on the graph of the function .

(b) The point is on the graph of the function .

Answer 2

Step 1:

The function and the point .

(a)

The point should satisfies the function .

Substitute in the function.

.

Hence, the point is on the graph of function .

Step 2:

(b)

Find .

The function .

Substitute in the function.

.

Hence, the point is on the graph of function .

Solution :

(a) The point is on the graph of the function .

(b) The point is on the graph of the function .

Answer 3

Step 1 :

(c)

Find the value of .

The function .

Here, .

The values of are .

The points are on the graph of function .

Step 2 :

(d)

The function is .

Since the function is a quadratic function , all possible real values of is the domain of .

The domain of the function is .

Solution :

(c) The points are on the graph of function .

(d) The domain of the function is .

Answer 4

Step 1 :

(e)

The function .

Find the - intercept by substituting  in the function.

Solve the equation.

The - intercepts are .

Step 2 :

(f)

The function .

Find the - intercept by substituting in the function.

The - intercept is .

Solution :

(e) The - intercepts are .

(f) The - intercept is .