(a) f(x) = 3x - 5. Find:
(i) f(7)
(ii) f(-1)
(b) Draw the graph of the function g: x ↦ 2x² - 2x - 5 in the domain -2 ≤ x ≤ 3, where x ∈ ℝ.
(i) Use the g... show full transcript
Worked Solution & Example Answer:(a) f(x) = 3x - 5 - Junior Cycle Mathematics - Question 14 - 2014
Step 1
Find f(7)
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Answer
To find f(7), we substitute x = 7 in the function f(x):
f(7)=3(7)−5=21−5=16
Step 2
Find f(-1)
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Answer
To find f(-1), we substitute x = -1 in the function f(x):
f(−1)=3(−1)−5=−3−5=−8
Step 3
Draw the graph of g: x ↦ 2x² - 2x - 5 in the domain -2 ≤ x ≤ 3
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Answer
The function g(x) = 2x² - 2x - 5 is a quadratic equation. To draw the graph:
Calculate the vertex of the parabola.
Determine y-values by substituting x-values in the domain.
Plot the points on the graph and sketch the curve, considering that it opens upwards.
Step 4
Use the graph drawn in (b)(i) to estimate the value of 2x² - 2x - 5 when x = 0.5
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From the graph, by locating x = 0.5, we observe that g(0.5) is approximately -5.5.
Step 5
The values of x for which g(x) = 0
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Answer
From the graph, we see that g(x) = 0 at approximately x = -1.1 and x = 2.1. This means the function intersects the x-axis at these values.
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