"Let f(x) = x2 \u2212 4. Let h(x) be a linear function such that h(\u22128) = 0 and h(3) = 11. (a) Determine a formula for h(x). (b) Calculate the values f (1), f (\u22121), f (2), f (\u22122), f (4), and f (\u22124). Explain why f (a) = f (\u2212a) for any positive real number a. (c) Graph y = f(x) and y = h(x) on the same grid. (d) For what values of x is (i) f(x) \u2264 0? (ii) h(x) \u2264 0? (iii) f(x) \u2264 h(x)? Give each of your answers as an inequality\/ inequalities."

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Let f(x) = x2 − 4

Math Apr 23, 2023

Let f(x) = x2 − 4. Let h(x) be a linear function such that h(−8) = 0 and h(3) = 11.
(a) Determine a formula for h(x).
(b) Calculate the values f (1), f (−1), f (2), f (−2), f (4), and f (−4). Explain why f (a) = f (−a) for any positive real number a.
(c) Graph y = f(x) and y = h(x) on the same grid.
(d) For what values of x is (i) f(x) ≤ 0? (ii) h(x) ≤ 0? (iii) f(x) ≤ h(x)? Give each of your answers as an
inequality/ inequalities.