How did the transformation of ()=f of , open x close . equals , x squared to ()=−g of , open x close . equals , x squared , minu

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2 years ago

12

s 3 in part (a) affect the intercepts?
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1 answer:

Nikolay [14] · Answer 1 · 2023-09-15T21:10:23+03:00

The intercepts are the points where the graph crosses the x or y-axis

The functions are given as:

$f(x) = x^2$

$g(x) = x^2 - 3$

Function f(x)

$f(x) = x^2$

The x-intercept is calculated as follows:

Set f(x) to 0

$x^2 = 0$

Solve for x

$x = 0$

The y-intercept is calculated as follows:

Set x to 0

$f(0) = 0^2$

$f(0) = 0$

Hence, the intercepts are 0

Function g(x)

$g(x) = x^2 - 3$

The x-intercept is calculated as follows:

Set g(x) to 0

$x^2 - 3 = 0$

Solve for x

$x^2 = 3$

$x = \±\sqrt 3$

The y-intercept is calculated as follows:

Set x to 0

$g(x) = x^2 - 3$

$g(0) = 0^2 - 3$

$g(0) = - 3$

The x-intercepts are $\±\sqrt 3$ , while the y-intercept is -3

By comparing the intercepts of f(x) and g(x),