Math  /  Algebra

Questionf(x)=2x2x1f(x)=2 x^{2}-x-1 (a) Is the point (2,9)(-2,9) on the graph of ff ? (b) If x=2x=2, what is f(x)f(x) ? What point is on the graph of ff ? (c) If f(x)=1f(x)=-1, what is xx ? What point(s) is/are on the graph of ff ? (d) What is the domain of ff ? (e) List the xx-intercept(s), if any, of the graph of f . (f) List the yy-intercept, if there is one, of the graph of f .

Studdy Solution
Find the y y -intercept by evaluating f(0) f(0) :
f(0)=2(0)201 f(0) = 2(0)^2 - 0 - 1 =1 = -1
The y y -intercept is (0,1)(0, -1).
The solutions are: (a) Yes, the point (2,9)(-2, 9) is on the graph of f f . (b) f(2)=5 f(2) = 5 , and the point (2,5)(2, 5) is on the graph. (c) x=0 x = 0 and x=12 x = \frac{1}{2} ; the points are (0,1)(0, -1) and (12,1)\left(\frac{1}{2}, -1\right). (d) The domain of f f is (,)(-\infty, \infty). (e) The x x -intercepts are (1,0)(1, 0) and (12,0)\left(-\frac{1}{2}, 0\right). (f) The y y -intercept is (0,1)(0, -1).

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