Mathematics 0580 · IGCSE · Graphs of functions

Graphs of functions — practice question

$f(x) = 2x^2 - 1$. For $-2 \le x \le 2$, the grid shows the graph of $y = f(x)$.
(a)[2]

Solve the equation $f(x) = 5$ by using the graph.

(b(i))[1]

Sketch the tangent to the graph of $y = f(x)$ at the point $(-1.5, 3.5)$.

(b(ii))[2]

Use your tangent line to estimate the gradient of $y = f(x)$ when $x = -1.5$.

(c(i))[1]

Fill in the table for $y = g(x)$.

(c(ii))[3]

On the opposite grid, draw the graph of $y = g(x)$ for $-2 \le x \le 2$.

(d(i))[2]

From your graphs, solve the equation $f(x) = g(x)$.

(d(ii))[1]

From your graphs, solve the inequality $f(x) < g(x)$.

(e(i))[1]

State the three values: $g(-3)$, $g(-5)$ and $g(-10)$.

(e(ii))[1]

Complete the statement. As $x$ decreases, $g(x)$ approaches the value ............

Worked solution & mark scheme

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